Question

How do you solve the simultaneous equations `y = x^2 + 3x` and `y = 6 - 2x`?

Answer 1

`color(red)(x=-6,y=18)` and `color(red)(x= 1,y=4)`

Explanation:

One way is to use the method of elimination.

Step 1. Enter the equations.

[1] `y=x^2+3x`
[2] `y=6-2x`

Step 2. Solve for one of the variables in terms of the other.

[2] `y=6-2x`

Since this is already done for us, we can go on to the next step.

Step 3. Substitute Equation 2 in Equation 1 and solve for `x`.

`6-2x=x^2+3x`

`x^2 +5x-6=0`

`(x+6)(x-1)=0`

`x+6=0` and `x-1=0`

`x=-6` and `x-1`

Step4. Substitute each value of `x` in Equation 2

If `x=-6`,
`y=6-2(-6) = 6+12`
`y=18`

If `x=1`,
`y=6-2(1) = 6-2`
`y=4`

Solutions: `x=-6,y=18` and `x= 1,y=4`

Check: Substitute the values of `x` and `y` in Equations 1 and 2.

Check **`1**: (`-6,18#)

`18=(-6)^2+3(-6)`
`18=36-18`
`18=18`

`18=6-2(-6)`
`18 = 6+12`
`18=18`

It checks!

Check **`2**: (`1,4#)

`4 = 1^2 +3(1)`
`4=1+3`
`4=4`

`4=6-2(1)`
`4 = 6-2`
`4=4`

It checks!

Our solutions are correct.