Question

Solve the system using the substitution method.
y-3x=2 and y=(x+1)^2-5


Solve the system using the elimination method.
y-3x=2 and y=(x+1)^2-5

Don't exactly understand how to do it either way.

Answer 1

y-3x=2
y=(x+1)^(2)-5

Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
y-3x=2
y=(x^(2)+2x+1)-5

Subtract 5 from 1 to get -4.
y-3x=2
y=x^(2)+2x-4

Since -3x does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3x to both sides.
y=3x+2
y=x^(2)+2x-4

Since the equation was solved for y, replace all occurrences of y in the other equations with the solution (3x+2).
y=3x+2
(3x+2)=x^(2)+2x-4

Remove the parentheses around the expression 3x+2.
y=3x+2
3x+2=x^(2)+2x-4

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
y=3x+2
x^(2)+2x-4=3x+2

Move all terms not containing x to the right-hand side of the equation.
y=3x+2
x^(2)-x-4=2

To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
y=3x+2
x^(2)-x-6=0

Factor the trinomial x^(2)-x-6.
y=3x+2
(x+2)(x-3)=0

Set each of the factors of the left-hand side of the equation equal to 0.
y=3x+2
x+2=0
x-3=0

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
y=3x+2
x=-2
x-3=0

Set each of the factors of the left-hand side of the equation equal to 0.
y=3x+2
x=-2
x-3=0

Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
y=3x+2
x=-2
x=3

The complete solution is the set of the individual solutions.
y=3x+2
x=-2,3

Multiply 3 by each term inside the parentheses.
For x=-2
y=-6+2

Add 2 to -6 to get -4.
For x=-2
y=-4

Multiply 3 by each term inside the parentheses.
For x=3
y=9+2

Add 2 to 9 to get 11.
For x=3
y=11

The final solution is the set of all solutions.
x=-2,y=-4
x=3,y=11

Hope this helps.

Answer 2

I know that the substitution would start off as \[(x+1)^{2}-5-3x=2\]
Right?

Answer 3

The solution is:
x=-2,y=-4
x=3,y=11

(-2, -4)
(3, 11)