Question

Solve this system of equation using the linear combinations method.
2x - 4y = 4
-3x + 10y = 14

Answer 1

[2x-4y=4] * -3
[-3x+10y=14] *2

-6x+12y=-12
-6x+20y=28
______________
0x-8y=-40
y= -40/-8
y= 5


2x-4(5)=4
2x-20=4
2x=24
x=12


This method is known as elimination

Answer 2

Thanks so much but , may I ask .. Why did you multiply by -3 ?

Answer 3

The goal of the elimination method is to eliminate a variable in order to solve for another variable. In this case I chose to eliminate x and solve for y. In order to eliminate x, you can multiply your first equation by the x value in your second equation (-3), and multiply your second equation by the x value in your first equation (2). Now the x values in both of you equations are -6, and you can subtract -6 - (-6) = 0 in order to eliminate x and solve for y.

Answer 4

Would you do the same if you were eliminating y and solving for x?

Answer 5

Exactly. Try eliminating y and solving for x

Answer 6

so if I was eliminating y , would I have to multiply the first equation by +4 and the second equation by -10 ?

Answer 7

Other way around. You would multiply the first equation by 10 and the second equation by -4. Remember that your goal is to get the y values in both of your equations equal to each other