A system of linear equations gives two equations that must be true for the same . Graph both equations as written in Desmos and click where their lines meet: the intersection satisfies both equations. Read the coordinates in order, first and second. Swapping them can turn the right point into a wrong choice.
Hints
- Hint 1
An intersection is a point shared by two lines. Its coordinates make both equations true at once. Where do the lines for the two given equations meet?
- Hint 2
Desmos can graph each equation as written, without rearranging it. After you click the intersection, read the first coordinate as and the second as .
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Graph both equations
Type and on separate Desmos lines. Each equation graphs as a line. Their intersection lies on both lines, so its coordinates make both equations true.
- Step 2
Read the ordered pair
Click the intersection, not a nearby grid mark. Desmos labels it : the first coordinate is , and the second is . So the ordered pair satisfying both equations is . Choice D.
Approach 2: Cancel a variable by hand
Step 1Make the y-terms opposites
The first equation has and the second has . In elimination, you make those terms opposites so they cancel when you add the equations. Multiply every term of the second equation by :
Distribute the :
- Step 2
Add the equations
The and cancel. Add both sides of the equations:
Combine like terms:
- Step 3
Find the first coordinate
Divide both sides by :
Simplify:
That's the first coordinate; you still need for the ordered pair.
- Step 4
Put x into an original equation
Use the shorter equation, . Replace with the value you found:
- Step 5
Find y and finish the pair
Subtract from both sides:
Divide by :
The first coordinate is and the second is , so . Choice D.