Question

How do you solve the simultaneous equations `4x + 3y = 9` and `3x - y = 10`?

Answer 1

`color(red)( x=3,y=-1)`

Explanation:

One way is to use the method of elimination.

Step 1. Enter the equations.

[1] `4x+3y=9`
[2] `3x-y=10`

Step 2. Prepare the equations.

Multiply each equation by numbers that give one variable the same coefficient in each equation.

Multiply Equation 2 by `3`.

[3] `9x-3y=30`

Step 2. Add Equations 1 and 3.

`13x=39`

[3] `x=3`

Step 3. Substitute Equation 3 in Equation 2.

`3x-y=10`
`3(3)-y=10`
`9-y=10`

`y=-1`

Solution: `x=3,y=-1`

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

`4x+3y=9`
`4(3) +3(-1)=9`
`12-3=9`
`9=9`

It checks!