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Mastering Simultaneous Equations

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Mastering Simultaneous Equations

Solve each system and show your reasoning. Give exact values unless a question asks for a decimal approximation. Check solutions in the original equations.

Linear systems and strategy

Begin with structure, then choose an efficient solving method.

1.Solve the system by elimination: 3x + 2y = 16 and 5x − 2y = 8. State the ordered pair and verify it in both equations.

2.Solve by substitution: y = 2x − 1 and x + y = 8. Give the ordered pair.

3.A student says the system 2x + 4y = 10 and x + 2y = 5 has exactly one solution because it contains two equations. Is the claim correct? Explain what the system’s solutions are.

4.Which statement describes the system 3x − 6y = 12 and x − 2y = 1?

It has one solution because the lines have different slopes.
It has no solution because the lines are parallel and distinct.
It has infinitely many solutions because one equation is a multiple of the other.
It has two solutions because both equations are linear.

Build and interpret a model

Use the data to form a system before solving.

Order

Adult tickets

Student tickets

Total paid

$57

$78

5.Use the ticket-order table to write a simultaneous system, then solve it. What is the price of each ticket?

6.A pair of numbers has sum 11. The sum of their squares is 65. Let the numbers be x and y. Set up and solve the system to find both possible ordered pairs.

Parameters and reasoning

Investigate how coefficients affect the number of solutions.

7.For what value of k does the system x + 2y = 5 and 3x + ky = 15 have infinitely many solutions? State why.

8.True or false? If two linear equations in two variables have different slopes, they have exactly one simultaneous solution. Give a brief justification.

TrueFalse

9.Match each system to its number of solutions. (i) x + y = 4; 2x + 2y = 8. (ii) x + y = 4; 2x + 2y = 10. (iii) x + y = 4; x − y = 2.

(i)
(ii)
(iii)

Exactly one solution
Infinitely many solutions
No solution

10.Challenge: Solve simultaneously x² + y² = 25 and y = x + 1. Give exact solutions and explain how you know you have found them all.

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Mastering Simultaneous Equations

Mastering Simultaneous Equations

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Build and interpret a model

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3 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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