Question

Consider the system of equations.

2x + 6y = -4

x - 2y = 18

(a) Dean rewrote the second equation as 3x – 6y = 54. What justification did he have for doing this?

(b) Dean combined the equation in Part (a) with the first equation in the system to get x = 10. Explain why Dean was justified in doing this.

(c) What is the solution of the system?

Answer 1

2x + 6y = -4 x - 2y = 18 times 3 on both sides equals
3x – 6y = 54

Answer 2

Why would Dean like three times the second equation ?

Answer 3

Waiting for a reply .....

Answer 4

Thanks, but what about B and C?

Answer 5

What about A, why would Dean want equation two multiplied by 3?

Hint: Look at the X and Y term numbers. What is special about them?

2x + 6y = -4
3x – 6y = 54

Answer 6

(A) He multiplied the second equation times 3.

(B) He was able to eliminate the Y's thanks to putting 6y in both of the equations. He then adds the left sides of equation 1 to the left side of equation 2. He repeats this with the right side, leaving 5x = 50. This means x = 10.

(C) the solution is (10, -4)

Right?

Answer 7

I would say that is very accurate.

But in part he multiplied the second equation by 3 in order to get the -6y term so that when he added the equation the y term would be eliminated.

Hence the process of solving equations is called the Elimination process.