Question

When Megan solved this system using the elimination method , she added the equations together and got the equation 4y = 16. Then she solved that equatio n 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 ? Show your work in the space provided. 2x + 3y = 20 - 2x + y = 4

Answer 1

Megan added the equations together but she subtract 4 instead of addition of 4. The correct solution is (1,6).

Explanation:

The given equations are

`2x+3y=20` ...(1)

`-2x+y=4` .... (2)

Add both equations to eliminate x.

`2x+3y-2x+y=20+4`

`4y=24`

Megan make a mistake in this step. She added the equations together but she subtract 4 instead of addition of 4.

Divide both sides by 4.

`y=6`

Put this value in equation (1).

`2x+3(6)=20`

`2x+18=20`

`2x=2`

Divide both sides by 2.

`x=1`

Therefore the correct solution is (1,6).