Systems of Equations

A system is two equations that must hold at the same time; its solution is the point (or points) that satisfies both. These are real, released Algebra I Regents questions — linear systems solved by substitution or elimination (including word problems you translate into a system), and linear-quadratic systems, where a line crosses a parabola in up to two places.

Every constructed-response item here is solved algebraically — set the expressions equal, or substitute, and solve. Work each one on paper, then reveal the official NYSED rubric and a worked model solution to score yourself; on these multi-step problems, the credit is in the work.

Question 1 of 30

Systems — linear-quadratic (solve algebraically)

Solve the system of equations algebraically for all values of

x

and

y

y = x^2 + 4x - 1

and

y = 2x + 7

Work it out on paper first — this is a show-your-work question. When you're done, reveal the rubric and model solution to score yourself.

Your score appears when you finish.

For teachers

Standard, common misconceptions, and suggested use will live here.