A system of equations gives two conditions that the same and must satisfy. Type both equations into Desmos and click their intersection, the point on both lines. Then use its coordinates to evaluate the expression the question asks for. Before solving by hand, also check whether adding or subtracting the equations builds that expression directly; don't stop at one coordinate.
Hints
- Hint 1
A solution to a system is one pair that makes both equations true. Graph the equations as written in Desmos. What does the point where their lines cross tell you?
- Hint 2
An ordered pair puts first and second. After you click the crossing point, use the first coordinate for and double the second coordinate in .
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Find the pair that satisfies both equations
Type both equations as written, one per line, and click their intersection. Desmos shows . A point on both lines makes both equations true, so and .
- Step 2
Evaluate the requested expression
The question asks for , not . Type on a third line; Desmos prints . So the value of is . Choice C.
Approach 2: Build the expression by subtraction
Step 1Subtract the equations
When the question asks for an expression, check whether combining the equations builds it directly. Here, subtracting the second equation from the first will give twice . Subtract the whole equation, including its right side:
- Step 2
Handle the minus sign
Distribute the minus sign across the parentheses. Subtracting adds :
- Step 3
Combine matching terms
Combine the -terms and the -terms to make one equation:
- Step 4
Get the expression asked for
Divide every term by :
So the requested value is . Choice C.