How do you solve 2x−y=6 and x+y=−3?

2 Answers
Evileyebrow
May 12, 2018

x=1
y=−4

Explanation:

There are 3 ways to solve this. Here is one way:

Elimination:

Line them up:

2x−y=6
x+y=−3

Add all that goes together:

2x+x=3x
−y+y=0
6−3=3

Put it back into an equation:

3x=3

x=1

Plug what x equals (1) into one of the previous equations:

(2∙1)−y=6
(−2)−y=6−2
−y=4ory=−4

1+y=−3
(−1)+y=−3−1
y=−4

Ruth N. · Stefan V.
May 12, 2018

x=1

y=−4

Explanation:

These are called simultaneous equations. Multiply both equations so they both have the same leading coefficient. Use the coefficient of x in one equation to multiply the entire equation of the other one. Do this for both.

[2x−y=6] ×1
[x+y=−3] ×2

Equals

2x−y=6
2x+2y=−6

Then subtract the two equations

2x−2x=0
[−y]−[2y]=−3y
6−[−6]=12

Result:

−3y=12

Simplify:

−y=4

so

y=−4

Replace the y in one of the equations with −4 to solve for x.

2x−y=6

2x−(−4)=6

2x+4=6

2x=6−4

2x=2

x=1

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