A system of equations asks for values that make both equations true. When two equations use the same and , graph them in Desmos and click their intersection, the point that solves both. In , the first coordinate is . If the -terms have opposite coefficients, adding the equations can also give you directly.
Hints
- Hint 1
A system needs one pair that makes both equations true. Desmos can graph each equation as written. Where would a pair that works in both appear on the graph?
- Hint 2
An intersection lies on both lines. Click where the lines cross to see the point's coordinates; reading grid squares instead can be imprecise.
- Hint 3
An ordered pair lists first and second. The question asks for one coordinate, not the whole point. Which coordinate should you enter?
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Graph both equations
Type and on separate Desmos lines, as written. Desmos draws two lines that cross once. That crossing is the solution: its coordinates make both equations true.
- Step 2
Read the requested coordinate
Click the intersection. Desmos shows , with the second coordinate rounded. In the ordered pair , is the first coordinate, so the requested value is . Grid in 7.
Approach 2: Cancel the y-terms by adding
Step 1Eliminate y
The -terms are opposites: and . In elimination, you add whole equations so one variable cancels. Add both left sides and both right sides:
Combine the remaining terms:
- Step 2
Find x
The equation gives , but the question asks for itself. Divide both sides by :
Evaluate:
You don't need to find . Grid in 7.