Math Core

This test covers checking and graphing solutions of systems, solving by substitution and by elimination, systems with no solution or infinitely many, and word problems.

Question 1

Which point is a solution of the system $y = 2x - 1$ and $x + y = 8$ ?

Question 2

The graph shows the system $y = x + 2$ and $y = -2x + 5$ . What is the solution?

y = x + 2y = -2x + 5Open in grapher →

Enter a point like (2, -3)

Question 3

How many solutions does the system $y = -3x + 4$ and $y = -3x - 1$ have?

Question 4

Solve the system $y = 4x$ and $2x + y = 18$ .

Enter a point like (2, -3)

Question 5

Solve the system $x = y + 6$ and $2x + 3y = 22$ .

Enter a point like (2, -3)

Question 6

Solve the system $x + y = 15$ and $x - y = 1$ .

Enter a point like (2, -3)

Question 7

Solve the system $3x + 2y = 4$ and $5x - 2y = 28$ .

Enter a point like (2, -3)

Question 8

Solve the system $2x + 5y = 1$ and $3x - 2y = 11$ .

Enter a point like (2, -3)

Question 9

How many solutions does the system $6x - 3y = 9$ and $y = 2x - 3$ have?

Question 10

The sum of two numbers is $52$ and their difference is $18$ . What are the two numbers?

Separate answers with commas, e.g. 2, -5

Question 11

A museum sold $40$ tickets for $390. Adult tickets cost $12 and child tickets cost $7. How many child tickets were sold?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

A bike shop has bicycles and tricycles on display. There are $25$ vehicles with $60$ wheels in all. How many tricycles are there?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

Plumber A charges $40 plus $25 per hour. Plumber B charges $70 plus $15 per hour. For what number of hours do they charge the same total, and what is that total? Answer as an ordered pair (hours, dollars).

Enter a point like (2, -3)