The sum of twice a number and another number is 24. The difference of twice the first number and the other number is 12. Which system would model this situation, and what is the solution?

Answer 1

x = 1st number and y = second number

2x + y = 24
2x - y = 12

Can you finish from here? Add the two equations to eliminate y and solve for x.

Then find y.

Be sure to check both x and y in both equations to be sure you are correct.

Answer 2

2 x + y = 24
y - 2x = 12

4 x = 12
x = 3

y = 24 - 6 = 18

check
6 + 18 = 24 yes
18 - 6 = 12 yes

note you could have written
2 x + y = 24
2 x - y = 12

2 y = 12
y = 6

2x + 6 = 24
x = 9

Answer 3

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