Answer:
(0, 6) and (-5, -9)
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!