At which point do the lines \(2x+y=16\) and \(x-2y=-8\) intersect on the graph?
Answer and explanation
Correct answer: \(\left(\frac{24}{5},\frac{32}{5}\right)\)
The intersection point is the common solution of both linear equations. From the first equation, \(y=16-2x\). Substituting this into the second equation gives \(x-2(16-2x)=-8\), so \(5x=24\) and \(x=\frac{24}{5}\). Therefore, \(y=16-2\left(\frac{24}{5}\right)=\frac{32}{5}\). Hence, the intersection point is \(\left(\frac{24}{5},\frac{32}{5}\right)\). Exam tip: verify the ordered pair in both original equations; \((4,8)\) satisfies the first equation but not the second.
Frequently asked questions
What is the correct answer to this question?
\(\left(\frac{24}{5},\frac{32}{5}\right)\)
Why is this the correct answer?
The intersection point is the common solution of both linear equations. From the first equation, \(y=16-2x\). Substituting this into the second equation gives \(x-2(16-2x)=-8\), so \(5x=24\) and \(x=\frac{24}{5}\). Therefore, \(y=16-2\left(\frac{24}{5}\right)=\frac{32}{5}\). Hence, the intersection point is \(\left(\frac{24}{5},\frac{32}{5}\right)\). Exam tip: verify the ordered pair in both original equations; \((4,8)\) satisfies the first equation but not the second.
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..
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