Question

How do you find the solution to the system of equations `9x +8y=16` and `3x+5y=10` by the elimination method?

Answer 1

`x=0, y=2`

Explanation:

To use the elimination method (also called the addition method), we make it so one of the variable members of both equations are equal so when we add or subtract them they cancel out.

In our case we look at both the 'x' and the 'y' member of both equations and see if we can multiply or divide the whole equation to make the terms equal on both. We can see that if we multiply `3x` by 3 we get `9x`, so we should multiply the whole second equation by 3:

`3(3x+5y)=3*10`
`9x+15y=30`

Now we can subtract the first equation from the modified second:
`(9x+15y)-(9x+8y)=30-16`
`9x+15y-9x-8y=14`
`15y-8y=14`
`7y=14`
`y=14/7`
`y=2`

At last, once we have the value of one of the variables, we just choose one of the original equations, plug in the value we now know, to find the value for the second variable. In this case:
`3x+5*2=10`
`3x+10=10`
`3x=10-10`
`3x=0`
`x=0`