Back to Solve systems of two linear equations in two variables algebraically — Problem 1 · Task Set 35

8.EE.C.8.b Tutor Intake -- Solving Systems Algebraically

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Grade 8·8 problems·~9 min·Common Core Math - Grade 8·standard·8-ee-c-8b

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Concepts

A system has the equations $3x + 2y = 5$ and $3x + 2y = 6$ . By
inspection (without doing algebra), how many solutions does this
system have?

No solution — the same expression $3x + 2y$ cannot equal both 5 and 6 at once.

One solution — substitute the expression from the first equation into the second equation and solve.

Infinitely many solutions, since both equations have the same left side.

It cannot be determined without graphing.