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

Answer:

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

Step-by-step 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).