A system is two equations about the same variables. Its solution must make both equations true, so graph both equations and read their intersection, the point on both lines. Type the equations as written in Desmos and click where the lines cross. A pair that fits only one equation is not a solution.
Hints
- Hint 1
A solution to a system must satisfy both equations at once. On a graph, where would you find a point that lies on both lines?
- Hint 2
Desmos can graph each equation as written; you don't need to rearrange either one. Click the intersection, where the lines cross, and read its first coordinate as and its second as .
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Graph the first equation
Type in Desmos. It draws a line of points that make the first equation true. A point on this line alone doesn't solve the system: it must also satisfy the other equation.
- Step 2
Read the point on both lines
Type on the next line and click where the lines cross. Desmos labels the intersection . This point is on both lines, so it makes both equations true. In the ordered pair , comes first and second. The solution is . Choice C.
Approach 2: Cancel the opposite terms
Step 1Add to remove
Use elimination: the and are opposites, so adding the equations removes . Add both sides:
Combine like terms:
- Step 2
Find
Divide both sides by :
- Step 3
Find and form the pair
Put into to get the second coordinate:
Subtract from both sides:
The solution ordered pair is . Choice C.