System of equations (substitution methods) can someone solve these problems x=3y-5; x+y=3 y=x; 3x+3y=18 y=3x+4; 5x-y=0

(1,2)

(3,3)

(-1/2, 11/2)

Step-by-step 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