Question

How do you solve the system of equations `x+ 4y = 12` and `x = 4y + 3`?

Answer 1

The solution to the system of equation is (-18, 7.5)

Explanation:

So there are a couple of ways we can solve for the system of equations. We can either do graphing, elimination or substitution method. Let's do substitution method as it seems easier to do for this type of problem.

So we have `x+4y = 12` and `x=4y+3`. So we can plug in `4y + 3` back into `x + 4y = 12`. So let do that.

`4y + 3 + 4y = 12`

So we will now combine the like terms and get this:

`8y + 3 = 12`

So we will now subtract 3 from both sides and get this:

`8y = 9`

Divide both sides by 8 and you get

y = `9/8` or 1.125

So let plug it back into `x=4y+3`

`x=4(9/8)+3` OR `x=4(1.125)+3`
`x=(9/2)+3` OR `x=4.5+3` -Multiply the number inside the ( ) by 4

`y=15/2` OR `y=7.5` - Add 3 to the fraction

But we need to plug it back into the equation to solve for x. So let plug it back into `x+4y=12`.

`x+4(7.5)=12`
`x+30=12`
`x=-18`

This equation works when plugging both x and y values back into the equation.

`-18+4(7.5) = ?`
`-18+30=?`
`-18+30 = 12`