Grade 10 Linear Systems Worksheet

This worksheet covers solving linear systems using various methods including graphing, substitution, and elimination, suitable for Grade 10 math students.

Grade 10 Math AlgebraLinear Systems

Use This Worksheet

Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.REI.C.5CCSS.MATH.CONTENT.HSA.REI.C.6

Topics

linear systemsalgebragrade 10math

8 sections · Free to use · Printable

← More Math worksheets for Grade 10

Grade 10 Linear Systems Practice

Name:

Date:

Score:

Read each question carefully and solve the linear systems using the indicated method or the method of your choice. Show all your work.

1. Solve the following linear system by graphing. Identify the solution.

Equation 1: y = 2x - 3

Equation 2: y = -x + 6

Solution: ( , )

2. Solve the following linear system using the substitution method.

Equation 1: x + 2y = 10

Equation 2: y = 3x - 9

Step 1: Substitute Equation 2 into Equation 1.

x + 2( ) = 10

Step 2: Solve for x. x =

Step 3: Substitute the value of x into Equation 2 to find y. y =

Solution: ( , )

3. Solve the following linear system using the elimination method.

Equation 1: 3x + 4y = 18

Equation 2: -3x + 2y = 6

Solution: ( , )

4. Which of the following linear systems has infinitely many solutions?

y = 2x + 1 y = 2x - 5

y = 3x - 2 y = -3x + 2

y = 4x + 7 2y = 8x + 14

y = x + 1 y = -x + 1

5. A linear system can have exactly two solutions.

True

False

6. The sum of two numbers is 25. Their difference is 7. Find the two numbers.