Question

How do you solve `–4x + 7y = –10` and `x – 5y = 9` using substitution?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Solve the second equation for `x`:

`x - 5y = 9`

`x - 5y + color(red)(5y) = 9 + color(red)(5y)`

`x - 0 = 9 + 5y`

`x = 9 + 5y`

Step 2) Substitute `9 + 5y` for `x` in the first equation and solve for `y`:

`-4x + 7y = -10`

`-4(9 + 5y) + 7y = -10`

`-36 - 20y + 7y = -10`

`-36 - 13y = -10`

`color(red)(36) - 36 - 13y = color(red)(36) - 10`

`0 - 13y = 26`

`-13y = 26`

`(-13y)/color(red)(-13) = 26/color(red)(-13)`

`(color(red)(cancel(color(black)(-13)))y)/cancel(color(red)(-13)) = -2`

`y = -2`

Step 3) Substitute `-2` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = 9 + 5y`

`x = 9 + (5 xx -2)`

`x = 9 - 10`

`x = -1`

The solution is `x = -1` and `y = -2`

Answer 2

`x=-1` and `y=-2`

Explanation:

`-4x+7y=-10`
`x-5y=9`

Using the second equation, we determine a value for `x`.

`x-5y=9`

Add `5y` to each side.

`x=9+5y`

In the first equation, substitute `x` with `color(red)((9+5y))`.

`-4x+7y=-10`

`-4color(red)((9+5y))+7y=-10`

Open the brackets and simplify. The product of a negative and a positive is a negative.

`color(red)(-36-20y)+7y=-10`

`-36-13y=-10`

Add `36` to both sides.

`-13y=26`

Divide both sides by `-13`.

`y=-2`

In the second equation, substitute `y` with `color(blue)(-2)`.

`x-5color(blue)((-2))=9`

Open the brackets and simplify. The product of two negatives is a positive.

`x+10=9`

Subtract `10` from both sides.

`x=-1`