Question

Solve the system
4x + 2y = 10
x = y + 13

Answer 1

Answer: (6,-7)

Explanation:

4x +2y = 10

x = y + 13 Substitute the value of x into the first equation to solve for y.

4(y + 13) +2y = 10 apply the distributive property on the left side

4y + 52 + 2y = 10 Combine like terms on the left side

6y + 52 = 10 Subtract 52 from both sides

-52 -52

6y = -42

y= -7

The value of y so input it into one of the equations to solve for x

4x + 2(-7) = 10

4x - 14 = 10

+14 +14

4x = 24

x= 6

Answer 2

`x = 6`

`y = -7`

Explanation:

We have the system of equations:

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

Let's solve by substituting. We know that
`x=y+13`, so we can substitute
`y+13` in as
`x` in the equation
`4x+2y=10`.

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

Simplify this down so that we have
`y` on one side of the equation:

`4y + 52 + 2y = 10\\\\6y + 52 = 10\\\\6y = -42\\\\y = -7`

Now that we know the value of
`y`, we can substitute it in to the equation
`x = y+13` to find
`x`.

`x = -7+13\\\\x = 6`

Hope this helped!