Question:
Which one of the following lines passes through the point of intersection of $x+y=5$ and $2x+y=7$? ________.
Which one of the following lines passes through the point of intersection of $x+y=5$ and $2x+y=7$? ________.
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Point of intersection is the simultaneous solution to the line equations.
Updated On: Jun 26, 2026
- $4x+3y=-1$
- $3x+2y=7$
- $4x-3y=-1$
- $4x+3y-2=0$
- $4x+3y+3=0$
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The Correct Option is C
Solution and Explanation
Step 1: Concept
Solve the system of equations to find the intersection point.
Step 2: Meaning
Subtract $x+y=5$ from $2x+y=7$ to get $x=2$. Substituting $x=2$ into $x+y=5$ gives $y=3$. The point is $(2, 3)$.
Step 3: Analysis
Check which option satisfies $(2, 3)$.
Option (C): $4(2) - 3(3) = 8 - 9 = -1$.
Step 4: Conclusion
The line $4x-3y=-1$ passes through $(2, 3)$. Final Answer: (C)
Solve the system of equations to find the intersection point.
Step 2: Meaning
Subtract $x+y=5$ from $2x+y=7$ to get $x=2$. Substituting $x=2$ into $x+y=5$ gives $y=3$. The point is $(2, 3)$.
Step 3: Analysis
Check which option satisfies $(2, 3)$.
Option (C): $4(2) - 3(3) = 8 - 9 = -1$.
Step 4: Conclusion
The line $4x-3y=-1$ passes through $(2, 3)$. Final Answer: (C)
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