Question

System of Equations

y=x-5
3x+y=7

Solve?

Answer 1

Y=x-5
-y=3x-7
Add them together
0=4x-12
12=4x
X=3
Y=-2

Answer 2

`\sf{y=x-5}`

`\sf{3x+y=7}`

Lets solve this by substitution.

Lets plug in y=x-5 into 3x+y=7

So:


`\sf{y=x-5}`

`\sf{3x+y=7}`

Plugging it in:


`\sf{3x+(x-5)=7}`

Solve for x by simplifying that:


`\sf{3x+x-5=7}`


`\sf{4x-5=7}`

Add 5 on both sides


`\sf{4x=12}`

Divide by 4 on both sides


`\sf{x=3}`

Now simply plug x=3 back into any equation and solve for y

So:

`\sf{y=x-5}`


`\sf{y=3-5}`

Simplify that:


`\sf{y=-2}`

So we are left with our final answer which is

`\boxed{\bf{(3,-2)}}`