Which ordered pair satisfies the system of equations below?
A system of equations gives two rules that the same ordered pair must satisfy. Enter each equation as written in Desmos and click the lines' intersection, where both rules hold. Read the point as , not ; reversing the coordinates can turn the right point into a wrong choice.
Hints
- Hint 1
An ordered pair lists the -value first and the -value second. To satisfy a system, the pair must make both equations true. Where would that pair appear on the graphs?
- Hint 2
Desmos can graph these equations without rewriting them as . Enter one equation per line, then click where the lines cross rather than estimating from the grid. Which coordinate in the point's label is ?
Step-by-step
Find the intersection in Desmos
Step 1Graph the first equation
Type into Desmos. It draws a line containing every pair that makes the first equation true. A system requires both equations to hold at once, so this line alone doesn't identify the answer.
- Step 2
Read the point on both lines
Add on the next line and click where the lines cross. Desmos labels the intersection . An intersection satisfies both equations, so the first coordinate is and the second is . The ordered pair that satisfies the system is . Choice D.