Solve the system using multiplication for the linear combination method. 6x – 3y = 3 –2x + 6y = 14 What is the solution to the system? (2, 1) (2, –3) (2, –1) (2, 3)

6x-3y=3
-2x+6y=14.
First step is multiply the top equation by 2, so you have
12x-6y=6
-2x+6y=14
-6y and +6y cancel each other out, so if you simplify, you have
10x=20, which is then solved by dividing each side by 10, and getting x=2.

Now plug x=2 into one of the equations (I chose the first)
6(2)-3y=3
12-3y=3
-3y=-9, divide each side by -3 and get y=3.
so your point is (2,3)

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ajeigbeibraheem ajeigbeibraheem · Answer 2 · 2021-11-05T11:26:23+01:00

By solving the system using multiplication for the linear combination method, the solution to the system is (2, 3). The last option is correct.

The multiplication for the linear combination method is usually known to be the elimination method.

Here, the two equations are placed under one another. Then, we multiply one of the equations with a number in such a way that if we subtract the two equations together, we will be left with two variables instead of three variables.

i.e.

6x – 3y = 3 ---- (1)
–2x + 6y = 14 ---- (2)

Let multiply equation (2) with (-3), we have:

-3( -2x + 6y = 14)
6x - 18y = -42 ----- (3)

Now, subtracting equation (1) from (3), we have:

6x - 3y = 3

-

6x - 18y = -42

0 + 15y = 45

15 y = 45

y = 45/15

y = 3

From equation (1), we will replace y with 3 to solve for x

So,

6x -3y = 3

6x - 3(3) = 3

6x - 9 = 3

6x = 9 + 3

6x = 12

x = 12/6

x = 2

Therefore, we can conclude that the solution to the system in order of (x,y) is (2, 3)

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