Question

4. When Megan solved this system using the elimination method, she added the equations together and got the equation 4y = 16. Then she solved that equation and got y = 4. Then she substituted 4 in the first equation for y and solved for x. She got x = 4. The point (4, 4) is not the correct solution. Please state in a complete sentence where she made her first mistake. What is the correct solution to the system? 2x + 3y = 20 -2x + y = 4

Answer 1

Hi there!

So, our two equations are:
2x + 3y = 20 and
-2x + y = 4

We can see that the x's will cancel out because they're the same number, opposite signs. Then we're left with 4y = 24.

Divide 24 by 4, which is 6.

y = 6, then we plug that in to the first equation for y:
2x + 3(6) = 20
2x + 18 = 20
2x = 2
x = 1

So, she made her first mistake when adding the equations, adding 20 and 4, she somehow got 16. 

The solution to the system is (1,6).

I hope I helped!