A system of equations asks for values that make both equations true. When the question asks for , type each equation into Desmos as written and click the intersection, where their lines meet. Check both equations, not just one: a point on one line might not lie on the other.
Hints
- Hint 1
Each equation draws a line of points that make it true. The solution must lie on both lines. Where would you look for a point they share?
- Hint 2
Click the intersection rather than estimating from the grid. In a pair , the first coordinate is and the second is .
Step-by-step
Approach 1: Find the intersection in Desmos
Step 1Graph the first equation
Type into Desmos as written. It draws a line, the straight graph of points that make this equation true. Don't pick a point yet; it must satisfy the other equation too.
- Step 2
Read the point shared by both lines
Add on the next line and click the intersection, where the lines meet. Desmos shows . That point is on both lines, so it makes both equations true. The first coordinate is and the second is , so the solution is . Choice D.
Approach 2: Cancel the opposite y-terms
Step 1Add the equations to remove y
The and are opposites. In elimination, you add equations so a variable cancels. Add their left sides and their right sides:
Combine matching terms:
- Step 2
Find x
Divide both sides by :
That's the first coordinate of the solution.
- Step 3
Use x to find y
Put into , which still has the other coordinate:
- Step 4
Finish the ordered pair
Subtract from both sides:
Write before , so the solution is . Choice D.