Task Sets: Understand that solutions to a system of two linear equations correspond to points of intersection of their graphs - Common Core Math - Grade 8

Fluency Practice

What does it mean for $(3, 7)$ to be the solution of a system of two equations?

$(3, 7)$ makes both equations true at the same time

$x = 3$ solves the first equation and $y = 7$ solves the second

$3$ comes from one equation and $7$ comes from the other

$(3, 7)$ makes at least one of the equations true

$A coordinate plane showing a solid line through (0,1) and (3,4) and a dashed line through (0,7) and (3,1); the two lines cross at a single grid point.$

The graph shows the lines $y = x + 1$ and $y = -2x + 7$ . Use the graph to find the solution of the system. Write your answer as an ordered pair $(x, y)$ .

$A coordinate plane showing a solid line through (0,-2) and (2,4) and a dashed line through (0,4) and (3,7); the lines cross at a single grid point.$

The graph shows the lines $y = 3x - 2$ and $y = x + 4$ . Use the graph to find the solution of the system. Write your answer as an ordered pair $(x, y)$ .

A student claims $(2, 5)$ is the solution of the system $y = 3x - 1$ and $y = x + 1$ . Verify by substitution. Enter the value of $y$ that $y = 3x - 1$ actually gives when $x = 2$ .

Without graphing, how many solutions does the system $y = 4x + 1$ and $y = 4x + 5$ have?

no solution

exactly one solution

infinitely many solutions

exactly two solutions

Exercises: Systems of Linear Equations — Why the Intersection Point Is the Solution

Recall / Warm-Up

Fluency Practice