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0. Review of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

1. Equations & Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs of Equations(0)

Graphs and Coordinates
(0)

Two-Variable Equations
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Lines
(0)

3. Functions(0)

Intro to Functions & Their Graphs
(0)

Common Functions
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Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

Dividing Polynomials
(0)

Zeros of Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential & Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Systems of Equations & Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

8. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

9. Sequences, Series, & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

10. Combinatorics & Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

7. Systems of Equations & Matrices

Two Variable Systems of Linear Equations

7. Systems of Equations & Matrices

Two Variable Systems of Linear Equations: Videos & Practice Problems

Video Lessons Practice Worksheet

129 problems

Problem types you want to practice:

Problem 31Multiple Choice

Solve the following system of equations by using your preferred method. Use the set notation to express their solution sets if the system has no solution or has infinitely many solutions.

Two linear equations: x + 7y = 9 and 2x - 3y = 18 for solving systems of equations.

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Problem 32Multiple Choice

Solve the following system of equations by using your preferred method. Use the set notation to express their solution sets if the system has no solution or has infinitely many solutions.

Two linear equations: y = 3x + 2 and -7x + y = -6 for solving systems.

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Problem 33Multiple Choice

Using the substitution method, solve the following system of equations.

System of equations for substitution method: 2x + 5y = -11, -x + y = 9.

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Problem 34Multiple Choice

Using the substitution method, solve the following system of equations.

System of equations for substitution method: x - 3y = 15 and x = 8y.

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Problem 35Multiple Choice

Using the substitution method, solve the following system of equations.

Two linear equations for solving a system using substitution method.

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Problem 36Multiple Choice

Using the substitution method, solve the following system of equations.

Two linear equations for a system: 5x - y = -30 and 4y - 2x = 30.

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Problem 37Multiple Choice

Using the substitution method, solve the following system of equations.

Two equations representing a system of linear equations for substitution method.

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Problem 38Multiple Choice

Using the substitution method, solve the following system of equations.

Two equations for solving a system: 5y = 12x + 15 and x + y = 3.

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Problem 39Multiple Choice

Using the elimination method, solve the following system of equations.

Two linear equations for solving a system using elimination method.

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Problem 40Multiple Choice

Using the elimination method, solve the following system of equations.

Two linear equations for solving a system using elimination method.

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Problem 41Multiple Choice

Using the elimination method, solve the following system of equations.

Two linear equations for elimination method: 4x + y = 13 and 3x - 5y = 4.

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Problem 42Multiple Choice

Using the elimination method, solve the following system of equations.

Two linear equations for solving a system using elimination method.

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Problem 43Multiple Choice

Solve the given system of linear equations using the substitution method.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"{\" close=\"\"><mtable columnalign=\"left\"><mtr><mtd><mn>4</mn><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>16</mn></mtd></mtr><mtr><mtd><mn>6</mn><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>5</mn><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>10</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$

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Problem 44Multiple Choice

Solve the given system of linear equations using the elimination method.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"{\" close=\"\"><mtable columnalign=\"left\"><mtr><mtd><mfrac><mrow><mi>x</mi><mo> </mo></mrow><mn>7</mn></mfrac><mo>+</mo><mfrac><mrow><mo> </mo><mi>y</mi><mo> </mo></mrow><mn>14</mn></mfrac><mo>=</mo><mo> </mo><mn>8</mn></mtd></mtr><mtr><mtd><mfrac><mrow><mi>x</mi><mo> </mo></mrow><mn>4</mn></mfrac><mo>+</mo><mfrac><mrow><mo> </mo><mi>y</mi><mo> </mo></mrow><mn>8</mn></mfrac><mo>=</mo><mo> </mo><mn>14</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$

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Problem 45Multiple Choice

Solve the given system of linear equations using the elimination method.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"{\" close=\"\"><mtable columnalign=\"left\"><mtr><mtd><mn>12</mn><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>8</mn><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>15</mn></mtd></mtr><mtr><mtd><mn>5</mn><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>3</mn><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$

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Problem 46Multiple Choice

Solve the following system of equations with two variables and determine if it is an inconsistent system or has infinitely many solutions. Write the solution set in terms of x if it has infinitely many solutions.

Two linear equations in a system: 3x - 7y = 4 and -9x + 21y = 4.

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Problem 47Multiple Choice

Two linear equations in a system: 7x - 7y - 15 = 0 and x - y + 13 = 0.

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Problem 48Multiple Choice

In standard form, write the system of equations associated with the graph shown.

Graph showing two linear equations with intersection points labeled.

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Problem 49Multiple Choice

In standard form, write the system of equations associated with the graph shown.

Graph showing two linear equations with intersection points labeled.

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Problem 50Multiple Choice

Solve the following system of equations, where x ≠ 0 and y ≠ 0:

System of equations for two variables x and y in college algebra.

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Problem 51Multiple Choice

Solve the following system of equations, where x ≠ 0 and y ≠ 0:

System of equations for two variables x and y in college algebra.

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Problem 52Multiple Choice

Using the elimination method, solve the following system of equations.

System of equations for two variables: x/4 + y/5 = 9 and 5x/4 + 7y/4 = 60.

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Problem 53Multiple Choice

Using the elimination method, solve the following system of equations.

System of equations for solving two variable linear equations using elimination method.

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Problem 54Multiple Choice

Find two numbers that sum up to 195 and have a difference of 3.

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Problem 55Multiple Choice

Enumerate the prices of a sack of dog food and a sack of cat food, if, in a pet shop, seven sacks of dog food and six bags of cat food were sold for \$627, while three sacks of dog food and eight sacks of cat food were sold for \$589 with no discounts applied.

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Problem 56Multiple Choice

Find the value(s) of q at which the system will have infinitely many solutions and no solution:

Two linear equations representing a system for college algebra, chapter 7.

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Problem 57Multiple Choice

Write an equation of a line that passes through (4, 6) and (-3, -8). Express the equation in slope-intercept form, y = mx + b. Make use of a system of equations in finding the values of m and b.

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Problem 58Multiple Choice

Write an equation of a parabola that passes through (-6, 7), (-3, 4), and (-1, 12). Express the equation in the form y = ax² + bx + c . Make use of a system of equations in finding the values of a, b, and c.

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Problem 59Multiple Choice

A pharmacy sells Azithromycin for $ 10 per tablet and Amoxicillin for $ 15 per tablet. The pharmacy receives an order for 50 tablets, but the customer forgot to specify how many of each item to send. If the pharmacy receives $ 650 for the order, how many tablets of Azithromycin and Amoxicillin should they send?

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Problem 60Multiple Choice

Solve the given system of equations.