Question

How do you solve this system of equations: `3x + 5y = 19 and 4x - y = 10`?

Answer 1

`x=3 and y=2`

Explanation:

I will solve your system by substitution (you can also solve this system by elimination).

`4x−y=10`
`3x+5y=19`

Step: Solve `4x−y=10` for `y`:

`4x−y+−4x=10+−4x" "` (add `-4x` to both sides)

`−y=−4x+10`

Divide by `-1`

`y=4x−10`

Step: Substitute `4x−10` for `y` in `3x+5y=19`:

`3x+5y=19`

`3x+5 (4x−10)=19`

`23x−50=19 " "`(simplify both sides of the equation)

`23x−50+50=19+50 " "`(add `50` to both sides)

`23x=69`

Divide both sides by `23`

`x=3`

Step: Substitute `3` for `x` in `y=4x−10`:

`y=4x−10`

`y=(4)(3)−10`

`y=2" "` (simplify both sides of the equation)