Task Sets: Solve systems of two linear equations in two variables algebraically - Common Core Math - Grade 8

Recall / Warm-Up

Is $(2, 5)$ a solution of the equation $3x + y = 11$ ?

Yes, because $3(2) + 5 = 11$

No, because $3(2) + 5 = 16$

Yes, because $x = 2$ is positive

No, because $5 \neq 11$

Which phrase describes solving a system "by inspection"?

recognizing the answer from the structure of the equations without full algebra

graphing both lines very carefully

guessing values until both equations work

always using elimination first

Solve the one-variable equation $5x + 1 = 11$ for $x$ .

Solve by substitution: $y = 2x + 1$ and $3x + y = 11$ . Enter the solution as an ordered pair $(x, y)$ .

Solve by substitution: $x + 3y = 7$ and $2x - y = 0$ . Enter the solution as an ordered pair $(x, y)$ .

Solve by elimination: $2x + 3y = 12$ and $2x - y = 4$ . Enter the solution as an ordered pair $(x, y)$ .

Solve by elimination: $3x + 2y = 16$ and $x - y = 2$ . Enter the solution as an ordered pair $(x, y)$ .

By inspection, how many solutions does the system $3x + 2y = 5$ and $3x + 2y = 6$ have?

no solution

exactly one solution

infinitely many solutions

exactly two solutions