Algebra · Practice

Systems of Equations — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

Solve the system and enter $x$ :

$x + y = 10, \quad x - y = 4$

Problem 2

Solve the system and enter $x$ :

$2x + y = 8, \quad x + y = 5$

Problem 3

Solve the system and enter $y$ :

$3x - 2y = 12, \quad x = 2$

Problem 4

Solve the system and enter $x$ :

$4x + 3y = 24, \quad 2x - y = 2$

Problem 5

Two numbers sum to $25$ and their difference is $7$ . What is the larger number?

Problem 6

Solve the system and enter the positive value of $x$ :

$x^2 + y = 10, \quad y = x + 4$

Problem 7

3 apples and 2 bananas cost $\$ 2.80 $. 2 apples and 3 bananas cost$ $2.70$.

Find the price of one apple in cents.

Problem 8

Solve the system and enter $z$ :

$x + y + z = 6, \quad x + 2y + 3z = 14, \quad x - y + z = 2$

Problem 9

Maximise $3x + 2y$ subject to $x + y \leq 8$ , $x \geq 1$ , $y \geq 2$ .

Problem 10

How many solutions does the system have?

$y = 2x + 1, \quad y = 2x - 3$