Question

How do you solve the system of equations `7x + 2y = 70` and `3x + 8y = 80`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve each equation for `8y`:

• Equation 1:

`7x + 2y = 70`

`7x - color(red)(7x) + 2y = 70 - color(red)(7x)`

`0 + 2y = 70 - 7x`

`2y = 70 - 7x`

`color(red)(4) xx 2y = color(red)(4)(70 - 7x)`

`8y = 280 - 28x`

• Equation 2:

`3x + 8y = 80`

`3x - color(red)(3x) + 8y = 80 - color(red)(3x)`

`0 + 8y = 80 - 3x`

`8y = 80 - 3x`

Step 2) Because the left side of each equation is the same we can equation the right side of each equation and solve for `x`:

`280 - 28x = 80 - 3x`

`280 - color(blue)(80) - 28x + color(red)(28x) = 80 - color(blue)(80) - 3x + color(red)(28x)`

`200 - 0 = 0 + (-3 + color(red)(28))x`

`200 = 25x`

`200/color(red)(25) = (25x)/color(red)(25)`

`8 = (color(red)(cancel(color(black)(25)))x)/cancel(color(red)(25))`

`8 = x`

`x = 8`

Step 3) Substitute `8` for `x` in the solution to either equation in Step 1 and solve for `y`:

`8y = 80 - 3x` becomes:

`8y = 80 - (3 xx 8)`

`8y = 80 - 24`

`8y = 56`

`(8y)/color(red)(8) = 56/color(red)(8)`

`(color(red)(cancel(color(black)(8)))y)/cancel(color(red)(8)) = 7`

`y = 7`

The Solution Is:

`x = 8` and `y = 7`

Or

`(8, 7)`