How to find the solution for a system of equations

Practice Questions

ACT Math › How to find the solution for a system of equations

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1

Jacob is 3 years older than Sarah, and Caroline is twice as old as Sarah. If Caroline is 28 years old, how many years old is Jacob?

2

Solve for x based on the following system of equations:

x + y = 5

2x + 3y = 20

3

If

and

Which of the following expresses in terms of ?

4

Find a solution to the system of equations:

2_x_ – y = 0

x + y = 3

5

Given the following two equations, solve for :

3a+2b=16 3a-2b=4

6

A store sells 17 coffee mugs for $169. Some of the mugs are $12 each and some are $7 each. How many $7 coffee mugs were sold?

7

Jenna's family owns a fruit stand. They began selling apples in 2010. In 2011 the number of apples sold increased by 100 apples. In 2012 they sold three times as many apples as they had in 2011, and in 2013 the number of apples increased by 200. If they sold 1700 apples in 2013, how many apples did they sell in 2011?

8

Suppose x2 + x – 6 = 0. Which of the following could be a value of x?

9

Sales for a business were more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were , what were sales, in millions of dollars, for the first year?

10

For what negative value of n does the system of equations yield no solutions?

3x + ny = 17
nx + (n + 6)y = 7

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