Question

Explain how to solve a system of equations by substitution

Answer 1

example:
let's assume we have a system of equations:

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

now.. we can take which one we want and solve for X or Y then to substitute to the other one...
let's take the first equation and solve for X

we have:
2x+2=4y
2x=4y-2
x=4/2 *y- 2/2
x=2y-1

now we have X .. let's substitute into the second equation...
y-3=2x

y-3=2(2y-1)
and solve it..
y-3=4y-2
y-4y=-2+3
-3y=1
y=\(-\frac13\)
so we have Y=- 1/3

now let's substitute in any equation we want..
let's substitute back into the first one and get X


2x+2=4y
2x+2=4*(-\(\large \frac13\))

2x+2=\(\large -\frac43\)

\(\large 2x=-\frac43-2\)

\(\large 2x=-\frac43-\frac63\)
2x=-10/3
x=-10/6

so we have

Y=-1/3
and X=-10/6