## If $$2x + y = 18$$ and $$3x = 17 + y,$$ what is the value of $$x?$$

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### If $$2x + y = 18$$ and $$3x = 17 + y,$$ what is the value of $$x?$$

by Vincen » Thu Mar 24, 2022 1:04 pm

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If $$2x + y = 18$$ and $$3x = 17 + y,$$ what is the value of $$x?$$

A. 1
B. 4
C. 7
D. 9
E. 13

Source: Veritas Prep

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### Re: If $$2x + y = 18$$ and $$3x = 17 + y,$$ what is the value of $$x?$$

by [email protected] » Fri Mar 25, 2022 6:03 am
Vincen wrote:
Thu Mar 24, 2022 1:04 pm
If $$2x + y = 18$$ and $$3x = 17 + y,$$ what is the value of $$x?$$

A. 1
B. 4
C. 7
D. 9
E. 13

Source: Veritas Prep
Let's use the elimination method...

GIVEN:
2x + y = 18
3x = 17 + y

Take 3x = 17 + y and subtract y from both sides to get: 3x - y = 17

We now have:
2x + y = 18
3x - y = 17

ADD the two equations to get: 5x = 35
Solve: x = 7