Consider the system of equations:
What is the value of ?
Two equations involving the same and form a system of equations: its solution must make both equations true. In Desmos, graph each equation as written and click where the lines cross. Read the second coordinate when asked for ; the first coordinate gives , while a point on only one line may not solve the system.
Hints
- Hint 1
A solution to a system must satisfy both equations at once. Each equation graphs as a line, so where should you look for a point that lies on both?
- Hint 2
An ordered pair lists coordinates as . After you click the lines’ intersection in Desmos, use the second number to answer a question about .
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Identify where a solution must lie
A solution is one pair that makes both equations true at once. On a graph, that pair lies where the two lines cross, not at a point on only one line.
- Step 2
Click the intersection and read
Type and on separate Desmos lines. Click their intersection; Desmos shows . An ordered pair lists first and second, so the value of is , not . Choice B.
Approach 2: Add the equations to eliminate
Step 1Cancel the opposite -terms
The and are opposites, so adding the equations cancels them. This is called elimination. Add both left sides and both right sides:
- Step 2
Find
Divide both sides by :
- Step 3
Put back into an equation
Use the first equation, . Substitute for :
- Step 4
Find the requested value
Subtract from both sides:
That is the value the question asks for. Choice B.