Back to Solve systems of two linear equations in two variables algebraically — Problem 2 · Task Set 35

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

This short check helps your tutor see where to start. Work each problem on
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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 student solves a system using elimination and arrives at
$x = -3/4$ . Their partner says the negative fraction means the
system has "no solution." Is the partner correct?

No — a solution can be any real number, including negative numbers and fractions. Check by substituting $x = -3/4$ into both original equations.

Yes — a fractional or negative result always signals no solution.

Yes, but only because the value is negative, not because it's a fraction.

It depends on whether the y-value also turns out to be a fraction.