Question

solve the following system of equations.
\

$$\begin{cases} y = x^2 + 7x - 5 \\ y = 6x + 7 \\end{cases}$$

if there is more than one solution, use the \or\ button.

Explanation:

Step1: Set equations equal

$x^2 + 7x - 5 = 6x + 7$

Step2: Rearrange to standard quadratic

$x^2 + 7x - 6x - 5 - 7 = 0$
$x^2 + x - 12 = 0$

Step3: Factor the quadratic

$(x + 4)(x - 3) = 0$

Step4: Solve for x

$x + 4 = 0 \implies x = -4$
$x - 3 = 0 \implies x = 3$

Step5: Find y for x=-4

$y = 6(-4) + 7 = -24 + 7 = -17$

Step6: Find y for x=3

$y = 6(3) + 7 = 18 + 7 = 25$

Answer:

$(x, y) = (-4, -17)$ or $(3, 25)$