Answer:
(1,2)
(3,3)
(-1/2, 11/2)
Explanation:
A system of equations is 2 or more equations for which the same x,y solution exists. We can solve the system in three ways: elimination, substitution, or graphing. Substitution can be used by substituting the value of one variable into the equation.
Pair x=3y-5 and x+y=3
Because x=3y-5, we can substitute 3y-5 into x in x+y=3
x+y=3
(3y-5)+y=3
3y-5+y=3
4y-5=3
4y-5+5=3+5
4y=8
y=2
We now substitute y=2 into x=3y-5.
x=3y-5
x=3(2)-5
x=6-5
x=1
Pair y=x and 3x+3y=18
Because y=x, we can substitute x into y in 3x+3y=18
3x+3y=18
3x+3x=18
6x=18
x=3
We now substitute x=3 into y=x.
y=3.
Pair y=-3x+4 and 5x-y=0
Because y=-3x+4, we can substitute -3x+4 into y in 5x-y=0
5x-y=0
5x-(-3x+4)=0
5x+3x+4=0
8x+4=0
8x=-4
x=-1/2
We now substitute x=-1/2 into y=-3x+4
y=-3x+4
y=-3(-1/2)+4
y=3/2+4
y=11/2