Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, June 2011)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Algebra 2/Trigonometry Regents, June 2011

Part IV: A correct answer will receive 6 credits. Partial credit is available.


39. Solve the following system of equations algebraically:

5 = y − x

4x² = −17x + y + 4

Answer:

Solve the first equation for y and then substitute into the second equation. Or subtract the first equation from the second equation.

Substitution:

y = x + 5
4x² = −17x + x + 5 + 4
4x² = −16x + 9

Elimination:

4x² = −17x + y + 4
5 = - x + y
4x² - 5 = −16x + 4
4x² = −16x + 9

Continuing:

4x² + 16x - 9 = 0

(ac) = -36

Factors of -36 that = 16 are +18 and -2.

4x² - 2x + 18x - 9 = 0

2x(2x - 1) + 9(2x - 1) = 0

(2x + 9)(2x - 1) = 0

2x + 9 = 0 or 2x - 1 = 0

2x = -9 or 2x = 1

x = -9/2 or x = 1/2

For each x, find the matching y:

x = -9/2, 5 = y - (-9/2), y = 1/2, (-9/2, 1/2)

x = 1/2, 5 = y - (1/2), y = 11/2, (1/2, 11/2)

End of Exam

More to come. Comments and questions welcome.

More Regents problems.

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