Solve the simultaneous equations

3x + 4y = 5

2x - 3y = 9

We label each equation

3x + 4y = 5 (1)

2x - 3y = 9 (2)

We now want to get rid of one of the variables (x or y). Lets get rid of x:

We need (1) and (2) to have the same number of x's so we multiple (1) by 2 and (2) by 3 so they both have 6 x's

6x + 8y = 10 (1) * 2

6x - 9y = 27 (2) * 3

Now to get rid of the x's we take one of the equations from the other. It is easier to do (2) * 3 - (1) * 2

6x - 9y = 27 (2) * 3

6x + 8y = 10 (1) * 2

-17y = 17

If we devide this equation by - 17 we get

y = - 1

We can plug this value of y into (1) to get

3x - 4 = 5

add 4 to both sides of the equation

3x = 9

Divide by 3

x = 3

Now to check put x and y into (2)

6 - (-3) = 9

As this is true, we have the solution

x = 3, y = - 1