In the following system of linear equations \(7x-15y=2\) and \(x+2y=3\), the value of \(x\) and \(y\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(x=\frac{49}{29}\) and \(y=\frac{19}{29}\)
The second equation gives \(x\) at once in terms of \(y\), so it is substituted into the first (substitution method), and the value of \(y\) found is then put back to give \(x\).
First equation: \(7x-15y=2\) (1)
The second equation, \(x+2y=3\), gives \(x=3-2y\) (2)
Putting (2) into (1): \(7(3-2y)-15y=2\)
\(21-29y=2\), which gives \(\displaystyle y=\frac{19}{29}\)
Putting this value of \(y\) into (2): \(\displaystyle x=3-\frac{38}{29}=\frac{49}{29}\)