Given
[1]color(white)("XXX")2x+4y=6XXX2x+4y=6
[2]color(white)("XXX")4x-3y=-10XXX4x−3y=−10
Method 1: By elimination
We note that if we multiply equation [1] by 22 the coefficient of xx will be the same as that of equation [2]
[3]color(white)("XXX")4x+8y=12XXX4x+8y=12
We can now eliminate the xx term by subtracting equation [2] from equation [3]
color(white)("XXX.."[x])4x+8y=color(white)("x..")12XXX..[x]4x+8y=x..12
color(white)("XXX")-(ul(4x-3y=-10))
[4]color(white)("XXXXXx..")11y=color(white)("x..")22
After dividing both sides by 11
[5]color(white)("XXX")y=2
Then substituting 2 for y in [1]
[6]color(white)("XXX")2x+4 * 2 =6
which simplifies as
[7]color(white)("XXX")2x=-2
or
[8]color(white)("XXX")x=-1
Method 2: By substitution
We note that we can divide both sides of [1] by 2 and then re-arrange the terms to get
[9]color(white)("XXX")x=3-2y
Now we can substitute (3-2y) for x in [2]
[10]color(white)("XXX")4 * (3-2y)-3y=-10
Simplifying [10]
[11]color(white)("XXX")12-8y-3y=-10
then
[12]color(white)("XXX")-11y=-22
and finally (after dividing both sides by 2
[13]color(white)("XXX")y=2
Substituting (2) for y back in [1] (or [9]) gives
[14}color(white)("XXX")x=-1
