Question 34·Easy·Systems of Two Linear Equations in Two Variables
A system of two linear equations is graphed in the -plane above.
Which choice gives the solution to the system of equations?
For graph-based systems, the solution is the point where the two lines cross. Use the grid to read the coordinates: read from the horizontal position and from the vertical position, then choose the ordered pair that matches .
Hints
Look for the shared point
Find the point where the two lines cross. That point is the solution to the system.
Use the grid
From the intersection point, trace straight to the -axis to read , and trace straight to the -axis to read .
Match the ordered pair format
Make sure you choose the point in the form , where comes first.
Desmos Guide
Plot the points shown on each line
In Desmos, plot the labeled points on the increasing line: (0,1) and (3,7). Then plot the labeled points on the decreasing line: (0,7) and (7,0).
Write an equation for each line
Find the slope of the increasing line from the two points: , so enter y=2x+1.
For the decreasing line, the slope is , so enter y=-x+7.
Find the intersection
Click the point where the two lines intersect. The intersection coordinates shown by Desmos match the correct choice.
Step-by-step Explanation
Find the intersection point
For a system of two linear equations, the solution is the point where the two lines intersect on the graph. Reading the grid at the intersection gives and .
Write the solution as an ordered pair
Therefore, the solution to the system is .