At which point do the lines \(x+3y=10\) and \(2x+3y=14\) intersect?
Answer and explanation
Correct answer: \((4,2)\)
Subtracting the first equation from the second gives \(x=4\). Substituting this into \(x+3y=10\) gives \(4+3y=10\), so \(y=2\). Therefore, the lines intersect at \((4,2)\). The distractor \((2,4)\) satisfies the first equation but gives \(2(2)+3(4)=16\neq14\), so it is not the common solution. In an exam, verify an intersection point in both equations.
Frequently asked questions
What is the correct answer to this question?
\((4,2)\)
Why is this the correct answer?
Subtracting the first equation from the second gives \(x=4\). Substituting this into \(x+3y=10\) gives \(4+3y=10\), so \(y=2\). Therefore, the lines intersect at \((4,2)\). The distractor \((2,4)\) satisfies the first equation but gives \(2(2)+3(4)=16\neq14\), so it is not the common solution. In an exam, verify an intersection point in both equations.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
