Given

[1]#color(white)("XXX")2x+4y=6#

[2]#color(white)("XXX")4x-3y=-10#

**Method 1: By elimination**

We note that if we multiply equation [1] by #2# the coefficient of #x# will be the same as that of equation [2]

[3]#color(white)("XXX")4x+8y=12#

We can now eliminate the #x# term by subtracting equation [2] from equation [3]

#color(white)("XXX.."[x])4x+8y=color(white)("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#