A system of linear equations gives two rules that must hold for the same pair . Graph both equations in Desmos as written and click where the lines meet. That point gives you both coordinates, but the question may ask for only one. Read the first coordinate for , not the second coordinate for .
Hints
- Hint 1
A system asks for one pair that works in both equations at once. Graph each given equation on its own Desmos line. Where would a pair that works in both appear?
- Hint 2
An intersection is where two graphs meet. Click that point to see its coordinates as . The first coordinate is ; the second is .
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Graph both equations
Type and on separate Desmos lines. Desmos draws two lines that meet. Keep the in the second equation: it says , not .
- Step 2
Read the value of
Click the intersection. Desmos labels it . A point where the lines meet satisfies both equations, so this is the solution pair . The question asks for , the first coordinate, so . Choice B.
Approach 2: See why substitution gives the same result
Step 1Replace with an equal expression
Substitution means replacing a variable with an expression equal to it. Since , replace the whole in the second equation:
- Step 2
Combine the -terms
Add the terms containing :
- Step 3
Move the constant
Add to both sides:
- Step 4
Find
Divide both sides by the coefficient of , the number multiplying : . So the system's -value is . Choice B.