Question

What is the solution set of the following system of equations?

Answer 1

Answer:

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

Step-by-step explanation:

y = 3x + 6

y = (x + 4)² - 10

*Perfect square trinomial rule: (a + b)² = a² + 2ab + b²

Using substitution, we can substitute the value of y from the first equation for the value of y for the second equation.

y = (x + 4)² - 10  ⇒  3x + 6 = (x + 4)² - 10

New equation:

3x + 6 = (x + 4)² - 10

Solve
3x + 6 = (x + 4)² - 10 <== simplify (x + 4)² using the rule listed above

3x + 6 = x² + 2(x)(4) + 4² - 10

3x + 6 = x² + 2(4x)  + 4(4) - 10

3x + 6 = x² + 8x + 16 - 10 <== combine any like terms

3x + 6 = x² + 8x + 6 <== subtract 6 from both sides

    - 6                 - 6

3x = x² + 8x <== rearrange

-x² - 8x + 3x = 0 <== combine any like terms

-x² -5x = 0 <== factor out -x

-x(x + 5) = 0

Find the zeros/x-intercepts of the equation:

-x = 0                          x + 5 = 0

/-1    /-1                           - 5    - 5

x = 0                            x = -5

Therefore, the zeros of the system of equations are: 0 and -5

Next, substitute the x values into y = 3x + 6.

For x = 0:

y = 3(0) + 6

y = 0 + 6

y = 6

(0, 6)

For x = -5:

y = 3(-5) + 6

y = -15 + 6

y = -9

(-5, -9)

The solution sets for the system of equations are: (0, 6) and (-5, -9)

Hope this helps!