A system of linear equations gives two rules that the same pair must satisfy. Graph both equations as written in Desmos and click their intersection, the point on both lines. Then read the coordinate the question requests: comes first and comes second. Swapping the coordinates or losing a minus sign changes the answer.
Hints
- Hint 1
A solution to a system must make both equations true. On a graph, that means the solution is the point where the two lines cross. You can type each equation into Desmos without rearranging it.
- Hint 2
An ordered pair lists coordinates in a fixed order: . After you click the crossing point, which number is in the second position? Keep its sign when you enter your answer.
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Graph both equations
Type and on separate lines in Desmos. Each equation graphs a line. A point where the lines cross satisfies both equations, so that point is the solution to the system.
- Step 2
Read the requested coordinate
Click the intersection. Desmos labels it . In an ordered pair , the second coordinate is , so . Don't enter : that's the first coordinate, . Grid in -1.
Approach 2: Eliminate by hand
Step 1Make the -coefficients match
The second equation has . Divide every term of the first equation by to get the same coefficient, the number multiplying :
- Step 2
Subtract to cancel
Subtract the whole new equation from . The matching terms cancel, leaving only :
The minus before the parentheses changes to , so .
- Step 3
Find
Divide both sides by :
The system's -value is . Grid in -1.