Question

What is the solution set of the following system of equations? y=3x+6 y=(x+4)^(2)-10 The solution tothe system is at (-5,-9). The solutjon to the system is at (5,21).

Answer 1

Systems of Equations

There are many strategies we can use to solve a system of equations, such as elimination or substitution.

• In elimination, we subtract or add the equations entirely to cancel out a variable.
• In substitution, we substitute one equation into the other.

Solution

`y=3x+6\\y=(x+4)^2-10`

Since y has already be isolated in both equations, we can just use substitution to equate them:

`3x+6=(x+4)^2-10`

Now, combine like terms:

`3x=(x+4)^2-16`

Expand the binomial:

`3x=x^2+8x+16-16\\3x=x^2+8x\\0=x^2+5x`

Find the zeroes:

`0=x(x+5)`

Therefore, x can be 0 or -5.

Now, we can plug these values of x back into one of the equations to determine the y coordinate:

`y=3x+6\\y=3(0)+6\\y=6`

Therefore, one solution is (0,6).

`y=3x+6\\y=3(-5)+6\\y=-15+6\\y=-9`

Another solutions is (-5,-9).

Answer

(0,6), (-5,-9)