Systems of Linear Equations in Two Variables Practice Problems

Determine whether the given ordered pairs satisfy the corresponding equations or not.

(i) (3, -2), 3x + 2y = 5

(ii) (3, -2), 7x + 5y = 11

A student is conducting an experiment in the laboratory. Determine how many mL of a 12% acid solution that the student must combine with 250 mL of a 24% acid solution to produce a 15% acid solution.

Solve the following system of equations. Express x or y in terms of a, if needed. Assume that a is not equal to 0.

Use any suitable method to solve the given system:

Use any suitable method to solve the given system:

Let x stand in for one number and y for the other. Create an equation system using the circumstances provided. Find the numbers by solving the system. 

The addition of the first number and the double of the other number is 22. 
The difference between these two numbers is -2.

Try to solve the following system of equations. Determine if the system has no solution, or infinitely many solutions (in which case express the answer using set notation.)  

Try to solve the following system of equations. Determine if the system has no solution, or infinitely many solutions (in which case express the answer using set notation.)  

Try to solve the following system of equations. Determine if the system has no solution, or infinitely many solutions (in which case express the answer using set notation.)  

Try to solve the following system of equations. Determine if the system has no solution, or infinitely many solutions (in which case express the answer using set notation.)  

Try to solve the following system of equations. Determine if the system has no solution, or infinitely many solutions (in which case express the answer using set notation.)  

Try to solve the following system of equations. Determine if the system has no solution, or infinitely many solutions (in which case express the answer using set notation.)  

Consider the given system of equations and solve using addition method:

Consider the given system of equations and solve using the addition method:

Consider the given system of equations and solve using addition method:

Consider the given system of equations and solve using addition method:

Consider the given system of equations and solve using addition method:

Consider the given system of equations and solve using the addition method:

Implement the substitution method to solve the system:

Implement the substitution method to solve the system:

Implement the substitution method to solve the system:

Implement the substitution method to solve the system:

Implement the substitution method to solve the system:

Implement the substitution method to solve the system:

Implement the substitution method to solve the system:

Find out whether the given ordered pair satisfies the system of equations shown.
(1, 3)

Find out whether the given ordered pair satisfies the system of equations shown.
(- 5, 1)

Find out whether the given ordered pair satisfies the system of equations shown.

 (-2, 6)

The difference between twice the length and 4 times the width of the lawn shown is 22 meters. Its perimeter is 52 meters. What is the length and width of the lawn?

Alice is mixing a 20% concentration of orange juice with an orange juice that has a higher concentration of 40% to have a 250-mL of orange juice mixture with 32% concentration. How many milliliters of each of the orange juice should be used?

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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. 

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

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

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

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

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

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

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

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.

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

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.

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.

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?