Question

Evaluate the simultaneous equations 2x + 4y = 13; x + y = 4 by using the Elimination
Method.

Answer 1

Look below

Explanation:

`A. 2x + 4y = 13 \\ B.x + y = 4`

Either remove the x or y

Lets do X first

In order to remove the 2 from eqaution A, we need to make the coefficient be the same for the x in the equation B.

We can multiply eqaution B by 2 in order to have the same x coefficient as eqaution A. In addition, we must make the 2 a negative (-2) in order to remove x.

`-2(x + y = 4)`

Now that we have the Xs ready for the elimination, we can proceed to answer for y

`2x + 4y = 13 + (-2x -2y = -8) \\\\2x - 2x = 0 \\4y - 2y = 2y \\13 - 8 = 5 \\\\2y = 5`

Now solve for y

`y = 2.5`

Now plug in 2.5 for either equation to find x ( in this case, B to make my life easier)

`x + 2.5 = 4\\x = 1.5`

Which in order to trust the other equation ( for some people to trust the answer for X -_-)

`2x + 4(2.5) = 13\\2x + 10 = 13\\2x = 3\\x = 1.5`

And from there, we conclude that x = 1.5 and y = 2.5

Now, we can get the same result if we eliminated y instead of x

(also this is copy and pasted from x because I am too lazy, get use to it)

In order to remove the 4 from eqaution A, we need to make the coefficient be the same for the y in the equation B.

We can multiply eqaution B by 4 in order to have the same x coefficient as eqaution A. In addition, we must make the 4 a negative (-4) in order to remove x.

`-4(x + y = 4)`

Now that we have the Ys ready for the elimination, we can proceed to answer for x

`2x + 4y = 13 + (-4x -4y = -16) \\\\2x - 4x = -2x \\4y - 4y = 0y \\13 - 16 = 5 \\\\-2x = -3`

Now solve for x

`\\x = 1.5`

Afterward, we are then able to do the same thing to find Y as we did previously in the previous section

Was this worth my time? No

Was it worth it? Yes

Why? I did this instead of a buddy's speech, so lol its funny to me lol