Question

Does anyone know how do solving systems of equations by elimination ?

Answer 1

Eliminate a single variable to find the value of another variable.

For example,

$-2x+y=3\\2x+4y=2$

Notice that -2x and 2x has the same "absolute" value right? -2x+2x = 0, that's how elimination work.

However, if you don't want to eliminate the "x", you can eliminate "y" instead.

Just simply multiply in.. From the equation above, we're going to eliminate y now.

However, both y in both equations are not the same (Doesn't have same coefficient) So we need to multiply in the equation that has the lesser coefficient (From both equations, the first equation has lesser coefficient)

So multiply 4 in -2x+y = 3 (To make the coefficient same.)

$-2x(4)+4(y)=4(3)\\-8x+4y=12$

Now we can eliminate y but we can't eliminate x because -8x and 2x both have the different variables.

$-8x+4y=12\\2x+4y=2$

However, it's 4y and 4y, not -4y and 4y. We can only eliminate as if the absolute of both variables are the same and the value must be opposite (Absolute of both variables are 4 but the value must be opposite aka one must be negative and another must be positive.)

So one of two 4y(s) must be negative, for me I'd choose -8x+4y=12 because -8x is in negative and I want it to be positive

So multiply "minus" in -8x+4y=12

$-(-8x+4y)=-12\\8x-4y=-12$

Now one is -4y, we can eliminate the y.

$8x-4y=-12\\2x+4y=2$

Then just simply eliminate y (-4y+4y = 0)

From x, 8x+2x = 10x and -12+2 = -10

10x = -10

x = -1 then substitute x in any equations but don't substitute in both equations, just one then you get the value of y.