```Question 621375
{{{system(3x - 8y = 2,4x - 4y = 32)}}}

A combination equation (made by multiplying equations times factors as needed and adding them) can replace one of the equations in a system to make an equivalent system.
{{{system(3x - 8y = 2,4x - 4y = 32)}}} --{{{matrix(2,1,"times (-1)", "times(2)")}}}--> {{{drawing(125,80,0,5,0,3.2,
locate(0.3,2.8,-3x + 8y = -2),locate(0.8,2,8x - 8y = 64),
line(0.2,1.1,4.8,1.1),locate(1.2,1,5x=64-2)
)}}} --> {{{5x=62}}} --> {{{5x/5=62/5}}} --> {{{highlight(x=62/5)}}}
{{{system(x=62/5,4x - 4y = 32)}}} --{{{matrix(2,1,"times 1", times (-1/4))}}}--> {{{drawing(125,125,0,5,-0.5,4,
locate(0.8,3.5,x),locate(2,3.5,"="),
locate(2.5,3.5,62/5),locate(0.2,2,-x+y=-8),
line(0.2,1.1,4.8,1.1),locate(1.5,1,y=62/5-8)
)}}} --> {{{y=62/5-40/5}}} --> {{{highlight(y=22/5)}}}

SOLVING BY SUBSTITUTION
{{{4x-4y=32}}} --(dividing both sides by 4)--> {{{x-y=8}}} --> {{{x-y+y=8+y}}} --> {{{x=y+8}}}
{{{3x-8y=2}}} --(multiplying both sides by (-1)) --> {{{-3x+8y=-2}}}
and substituting the expression for x found before
{{{-3x+8y=-2}}} --> {{{-3(y+8)-8y=-2}}} --> {{{-3y-24+8y=-2}}} --> {{{-24+5y=-2}}} --> {{{-24+5y+24=-2+24}}} --> {{{5y=22}}} --> {{{5y/5=2/52}}} --> {{{highlight(y=22/5)}}}
and that value can be substituted in {{{x=y+8}}} to get
{{{x=22/5+8}}} -->{{{x=22/5+40/5}}} --> {{{highlight(x=62/5)}}}```