Question

Solve the system by substitution.
4x + 2y = 10
x − y = 13

Answer 1

`\boxed{\tt (6,-7)}`

Explanation:

`\tt 4x + 2y = 10\\x - y = 13`

First Let's solve for x in x-y=13

`\tt x-y=13`

Add y to both sides:

`\tt x=13+y`

Now, Substitute x=13+y into 4x+2y=10:-

Let x=13+y

`\tt 4(13+y)+2y=10`

`\tt 52+6y=10`

Now, let's solve for y in 52+6y=10:-

`\tt 52+6y=10`

Subtract 52 from both sides:-

`\tt 6y=10-52`

`\tt 6y=-42`

Divide both sides by 6:-

`\tt \cfrac{6y}{6} =\cfrac{-42}{6}`

`\boxed{\tt y=-7}`

Now, we'll Substitute y=-7 into to x=13+y to find "x":-

`\tt x=13+y`

`\tt x=13+-7`

`\boxed{\tt x=6}`

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