A system of equations asks for one pair that makes two equations true at once. Graph both equations as written in Desmos, then click their intersection, the point where the lines meet. Read the coordinate the question requests: is the second coordinate, not a number you can take from either equation on its own.
Hints
- Hint 1
A solution must make both equations true for the same and . On a graph, where would you find a point that lies on both lines?
- Hint 2
Desmos can graph each equation as written, so you don't need to solve either one for . Click where the lines meet rather than estimating from grid squares.
- Hint 3
An ordered pair lists first and second. Once you have the intersection, which coordinate does the question ask you to use?
Step-by-step
Approach 1: Graph the system in Desmos
Step 1Graph the first equation
Type into Desmos. It draws the line of points that make this equation true. One line gives possible pairs, but you still need a pair that fits the other equation.
- Step 2
Find the point shared by both lines
Type on the next line. Desmos draws a second line. The intersection, where the lines meet, is the only point on both, so it's the solution to the system.
- Step 3
Read the requested coordinate
Click the intersection. Desmos labels it . In the ordered pair , comes first and comes second. Read the coordinate the question asks for, so . Choice C.
Approach 2: Eliminate to find directly
Step 1Make the first -term
To find directly, make the -terms cancel. Multiply every term on both sides of the first equation by :
- Step 2
Make the second -term
Multiply every term on both sides of the second equation by . The opposite -terms will cancel when you add:
- Step 3
Add to remove
Add the two new equations. Since , only remains:
- Step 4
Solve for the requested value
Divide both sides by to get alone:
So the value of is . Choice C.