Two equations with the same and form a system of equations. Graph both in Desmos and click their intersection, the point that makes both equations true. The intersection gives you and , but you still need to calculate the expression the question asks for. Graph labels can be rounded, so use the answer choices to interpret a nearby result.
Hints
- Hint 1
The intersection is the point on both lines, so its coordinates solve both equations. Type each equation into Desmos as written and click where the lines cross. Which coordinate represents ?
- Hint 2
An ordered pair lists first and second. Multiply the first coordinate by to find . If Desmos rounded the coordinate, expect your calculation to be close to an answer choice.
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Find the value of x
Type both equations into Desmos as written, then click where their lines cross. Desmos labels the intersection approximately . The first coordinate is , so .
- Step 2
Calculate the requested expression
The question asks for , not alone. Type ; Desmos shows . That is slightly below because the clicked point's coordinate was rounded, so matches . Choice B.
Approach 2: Build 7x directly by elimination
Step 1Multiply the second equation by 3
The first equation has , while the second has . Triple the whole second equation, including its right side, to make . Multiply by :
- Step 2
Distribute on both sides
Distribute through the scaled equation:
- Step 3
Add the equations to cancel y
Elimination means adding equations so one variable disappears. Add the first equation to the scaled second equation; and cancel:
- Step 4
Combine like terms
Combine like terms:
- Step 5
Reach the requested value
The question wants , which is half of . Divide both sides by :
So the value of is . Choice B.