Question

Solve the system of equations.

y = 3x + 2
y = x^2 – 4x + 2

A. (0, –2) and (–7, –23)
B. (–7, –23) and (0, 2)
C. (–7, 23) and (0, –2)
D. (0, 2) and (7, 23)

Answer 1

D. (0, 2) and (7, 23)

Explanation:

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Answer 2

When you solve a system of equations you are determining where the curves intersect in a coordinate plane. These places of intersection share the exact same x and y points. Since both equations above are already solved for y, and since the y values for each will be the same, let's set them equal to each other and solve for x.
`3x+2= x^(2) -4x+2`. The way to solve for x is to combine like terms, set the resulting polynomial equal to 0, and factor to find x. Doing that gives us
`x^(2) -7x=0`. We can factor a common x out of those terms to get 0 = x(x-7). By the Zero Product Property theorem, x = 0 or x-7 = 0. So x = 0 and x = 7. Sub those x values back in to solve for y. y = 3(0)+2 and y = 2. So one of our coordinates is (0, 2). y = 3(7)+2 so y = 23. The other coordinate is (7, 23). Those choices are found together in D above.