Question

How do you solve this system of equations: `8x + 3y =7 and 4x + 3y = 2`?

Answer 1

See a solution process below:

Explanation:

Step 1: Solve each equation for `3y`:

• Equation 1:

`8x - color(red)(8x) + 3y = 7 - color(red)(8x)`

`0 + 3y = 7 - 8x`

`3y = 7 - 8x`

• Equation 2:

`4x - color(red)(4x) + 3y = 2 - color(red)(4x)`

`0 + 3y = 2 - 4x`

`3y = 2 - 4x`

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

`7 - 8x = 2 - 4x`

`7 - color(blue)(2) - 8x + color(red)(8x) = 2 - color(blue)(2) - 4x + color(red)(8x)`

`5 - 0 = 0 + (-4 + color(red)(8))x`

`5 = 4x`

`5/color(red)(4) = (4x)/color(red)(4)`

`5/4 = (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))`

`5/4 = x`

`x = 5/4`

Step 3: Substitute `5/4` for `x` into the solution to either equation in Step 1 and solve for `y`:

`3y = 7 - 8x` becomes:

`3y = 7 - (8 xx 5/4)`

`3y = 7 - (color(red)(cancel(color(black)(8)))2 xx 5/color(red)(cancel(color(black)(4))))`

`3y = 7 - (2 xx 5)`

`3y = 7 - 10`

`3y = -3`

`(3y)/color(red)(3) = -3/color(red)(3)`

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = -1`

`y = -1`

The Solution Is: `x = 5/4` and `y = -1` or `(5/4, -1)`