Question

Elimination. help, please?

x+2y=7
+3x-2y=-3

Answer 1

x=1, y=3

Explanation:

To use elimination, you need to multiply an entire one of the equations so that the coefficient of one of the variables is equal to the opposite of the coefficient of the variable in the other equation. I know that sounds a little confusing, so I'm just going to show you what this means.

We see in the second equation the coefficient of x is 3, so we can make the coefficient of x in the first equation -3 by multiplying the entire first equation by -3. By multiplying the entire equation by one number, we are able to keep the equation balanced.

`-3(x+2y=7)=>-3x-6y=-21`

Now that we have this version of the equation, we can add the first half of each side of the equation and the second half of each side of the equation to get one, giant conglomerate equation.

`+3x-2y=-3`
`(-3x-6y=-21)/(0x-8y=-24)`

Using this combined equation, we can now solve for y to get that y = 3. Finally, we can plug this value for y back into one of our previous equations and solve.

`x+2(3)=7`
`x+6=7`
`x=1`

Finally, to verify, we can plug our values of x and y into the other equation and make sure that it works.

`3(1)-2(3)=-3`
`3-6=-3`
`-3=-3`

Note: if you are trying to find this point graphically, you can rewrite it in coordinate notation as (1, 3).