1. Fundamental Concepts of Algebra

2. Equations and Inequalities

3. Functions and Graphs

4. Polynomial and Rational Functions

5. Exponential and Logarithmic Functions

6. Systems of Equations and Inequalities

7. Matrices and Determinants

8. Conic Sections

9. Sequences, Induction, and Probability

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Solve each system in Exercises 25–26. (x+2)/6 − (y+4)/3 + z/2 = 0, (x+1)/2 + (y−1)/2 − z/4 = 9/2, (x−5)/4 + (y+1)/3 + (z−2)/2 = 19/4

Solve each system in Exercises 5–18. 3x+2y−3z=−2, 2x−5y+2z=−2, 4x−3y+4z=  10

Solve each system in Exercises 5–18. 3(2x+y)+5z=−1, 2(x−3y+4z)=−9, 4(1+x)=−3(z−3y)

❖ Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 1 ❖

Solve each problem. See Examples 5 and 9. Solve the system of equations (4), (5), and (6) from Example 9.
25x + 40y + 20z = 2200 (4)
4x + 2y + 3z = 280 (5)
3x + 2y + z = 180 (6)

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (4, 1, 2) x−2y=2, 2x+3y=11, y−4z=−7

In Exercises 19–22, find the quadratic function y = ax^2+bx+c whose graph passes through the given points. (−1, 6), (1, 4), (2, 9)

Using Substitution to Solve a Linear System of Three Equations and Three Variables

Find the quadratic function y = ax^2 + bx + c whose graph passes through the points (1, 4), (3, 20), and (-2, 25).

How to Check a Solution to a Linear System of 3 Equations and 3 Unknowns

System of 3 Equations with 3 Unknowns Application - Concentration Problem

Solve each system in Exercises 5–18. 2x+y=2, x+y−z=4, 3x+2y+z=0

Solve each system in Exercises 5–18. x+y=−4, y−z=1, 2x+y+3z=−21

System of 3 Equations, 3 Unknowns Using Elimination- Ex 2

Solve each problem. See Examples 5 and 9. A cashier has a total of 30 bills, made up of ones, fives, and twenties. The number of twenties is 9 more than the number of ones. The total value of the money is $351. How many of each denomination of bill are there?

Solve each system in Exercises 5–18. x+0y+2z=11, x+0y+3z=14, x+2y−0z=5

Solve each system in Exercises 5–18. 2x−4y+3z=17, x+2y−z=0, 4x−y−z=6

Using Elimination to Solve a Linear System of Three Equations and Three Variables

Solve Problems Using Systems in 3 Variables

Systems of Linear Equations in 3 Variables

System of 3 Equations with 3 Unknowns Application - Ticket Sales

Solve Linear System in 3 Variables - Football Word Problem

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (2,−1, 3) x+  y+0z=4, x−2y−0z=1, 2x−y−2z=−1

Solving a Dependent System of Linear Equations involving 3 Variables

Solving a 3 x 3 System of Equations Using the Inverse

Solve each system in Exercises 5–18. 4x−0y+2z=11, x+2y−z=−1, 2x+2y−3z=−1

Exercises 57–59 will help you prepare for the material covered in the next section. Solve: A + B = 3, 2A - 2B + C = 17, 4A - 2C =14

Solve each problem. See Examples 5 and 9. A sparkling-water distributor wants to make up 300 gal of sparkling water to sell for $6.00 per gallon. She wishes to mix three grades of water selling for $9.00, $3.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as of the $3.00 water. How many gallons of each should she use?

Word Problem: System of Linear Equations, 3 Unknowns, 3 Variables

In Exercises 19–22, find the quadratic function y = ax^2+bx+c whose graph passes through the given points. (−1,−4), (1,−2), (2, 5)

Solve each problem. See Examples 5 and 9. The sum of the measures of the angles of any triangle is 180°. In a certain triangle, the largest angle measures 55° less than twice the medium angle, and the smallest angle measures 25° less than the medium angle. Find the measures of all three angles.

Solve each system in Exercises 12–13.  The  is a piecewise function

Solve by eliminating variables: <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/622793c3172f7911-1678243504297.jpg" style="width: 254px;">

Solve each system in Exercises 25–26. (x+3)/2 − (y−1)/2 + (z+2)/4 = 3/2, (x−5)/2 + (y+1)/3 − z/4 = − 25/6, (x−3)/4 − (y+1)/2 + (z−3)/2= − 5/2

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

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Graph a Linear Inequality in Two Variables

Graph a Nonlinear Inequality in Two Variables

Use Mathematical Models Involving Linear Inequalities

Graph a System of Inequalities

Systems of Inequalities

Determine Whether an Ordered Pair is a Solution of a Linear System

Solve Linear Systems by Substitution

Solve Linear Systems by Addition

Identify Systems That Don't Have One Ordered-Pair Solution

Solve Problems Using Systems of Linear Equations

Systems of Linear Equations in Two Variables

Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

Use Inequalities to Describe Limitations in a Situation

Use Linear Programming to Solve Problems

Linear Programming

Decompose P / Q, Where Q Has Only Distinct Linear Factors

Decompose P / Q, Where Q Has Repeated Linear Factors

Decompose P / Q, Where Q Has a Nonrepeated Prime Quadratic Factor

Decompose P / Q, Where Q Has a Prime, Repeated Quadratic Factor

Partial Fractions

Recognize Systems of Nonlinear Equations in Two Variables

Solve Nonlinear Systems by Substitution

Solve Nonlinear Systems by Addition

Solve Problems Using Systems of Nonlinear Equations

Systems of Nonlinear Equations in Two Variables

Verify Solution of a System of Linear Equations in 3 Variables

Solve Systems of Linear Equations in Three Variables

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