Question

The elimination method was used to solve the following system of equations:

x2 – y = –3
x2 + y2 = 9

Which of the following is the correct y-coordinate of the solution? (5 points)
0
1
3
-4

Answer 1

(c) 3

Explanation:

You want the y-value of the solution to the equations ...

• x² -y = -3
• x² +y² = 9

Elimination

We are interested in the value of y, so it can be useful to eliminate x from the equation(s). The x² term appears in both, so it is convenient to subtract the first equation from the second.

(x² +y²) -(x² -y) = (9) -(-3)

y² +y = 12

y² +y -12 = 0 . . . . . . subtract 12

(y +4)(y -3) = 0 . . . . . factor

y = -4 or +3 . . . . . . . . values that make the factors zero

Domain

Solving the first equation for y, we find ...

x² +3 = y . . . . . . . add y+3

We know that x² cannot be negative, so this tells us the values of y will be ...

y ≥ 3

Of the two solutions we found above, the value -4 is extraneous (not in the domain of y).

The y-coordinate of the solution is 3, choice C.

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Additional comment

The solution is the point of intersection of the two curves shown in the attachment. The y-coordinate of that point is 3.

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