Solve the system of equations: y = 2x - 4 y= x^2 - 4

Question

asked Jun 6, 2022 108k views

1 Answer

Mads Hansen · Answer 1 · 2022-06-10T04:56:51+0000

Answer:

correct question

$\\ \longmapsto$ y=2x -4

$\\ \longmapsto$ y=x²-4

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The two intersections would be (3, 10) and (-2, 0)

Explanation:

To solve this system of equations, set the two equations equal to each other and solve for x.

$\\ \mapsto$ 2x + 4 = x² + x - 2

$\\ \mapsto$ 2x = x² + x - 6

$\\ \mapsto$ 0 = x² - x - 6

$\\ \mapsto$ 0 = (x - 3)(x + 2)

Now set the parenthesis equal to zero to get the x values.

$\\ \mapsto$ x - 3 = 0

$\\ \mapsto$ x = 3

$\\ \mapsto$ x + 2 = 0

$\\ \longmapsto$ x = -2

Now we know the x values of each interception. We can find the y values by plugging into either equation.

$\\ \mapsto$ y = 2x + 4

$\\ \mapsto$ y = 2(3) + 4

$\\ \mapsto$ y = 6 + 4

$\\ \longmapsto$ y = 10

$\\ \mapsto$ y = 2x + 4

$\\ \mapsto$ y = 2(-2) + 4

$\\ \mapsto$ y = -4 + 4

$\\ \longmapsto$ y = 0