Question

How do you solve the system `5x + 6y = 2` and `-2x + 3y = 37`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve each equation for `6y`:

• Equation 1:

`5x + 6y = 2`

`5x - color(red)(5x) + 6y = 2 - color(red)(5x)`

`0 + 6y = 2 - 5x`

`6y = 2 - 5x`

• Equation 2:

`-2x + 3y = 37`

`-2x + color(red)(2x) + 3y = 37 + color(red)(2x)`

`0 + 3y = 37 + 2x`

`3y = 37 + 2x`

`color(red)(2) xx 3y = color(red)(2)(37 + 2x)`

`6y = (color(red)(2) xx 37) + (color(red)(2) xx 2x)`

`6y = 74 + 4x`

Step 2) Because the left side of both equations are the same we can equate the right side of both equations and solve for `x`:

`2 - 5x = 74 + 4x`

`2 - color(red)(2) - 5x - color(blue)(4x) = 74 - color(red)(2) + 4x - color(blue)(4x)`

`0 + (-5 - color(blue)(4))x = 72 + 0`

`-9x = 72`

`(-9x)/color(red)(-9) = 72/color(red)(-9)`

`(color(red)(cancel(color(black)(-9)))x)/cancel(color(red)(-9)) = -8`

`x = -8`

Step 3) Substitute `-8` into either of the equations in Step 1 and solve for `y`:

`3y = 37 + 2x` becomes:

`3y = 37 + (-8 xx 2)`

`3y = 37 - 16`

`3y = 21`

`(3y)/color(red)(3) = 21/color(red)(3)`

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = 7`

`y = 7`

The Solution Is:

`x = -8` and `y = 7`

Or

`(-8, 7)`