Mathematics 2019 JAMB Past Questions - Question 36: IF 5(x+2y) =5 and 4(x+3y) =16, find 3(x+y)

Correct Answer

B

Explanation

To solve for \(3(x+y)\), we can first solve the given system of equations:\[5(x+2y) = 5\]\[4(x+3y) = 16\]We can start by solving the first equation for \(x+2y\):\[x+2y = 1\]Next, we solve the second equation for \(x+3y\):\[x+3y = 4\]Now, we can add the two equations together to get \(2x+5y\):\[2x+5y = 5\]Solving for \(x\) in terms of \(y\), we get:\[x = 5 - 5y\]Now, we can substitute this value of \(x\) into the equation \(x+2y = 1\) to solve for \(y\):\[5 - 5y + 2y = 1\]\[5 - 3y = 1\]\[-3y = 1 - 5\]\[-3y = -4\]\[y = \frac{-4}{-3}\]\[y = \frac{4}{3}\]Now that we have found the value of \(y\), we can substitute it back into the equation \(x+3y = 4\) to solve for \(x\):\[x + 3(\frac{4}{3}) = 4\]\[x + 4 = 4\]\[x = 4 - 4\]\[x = 0\]Now that we have found the values of \(x\) and \(y\), we can find \(3(x+y)\):\[3(0 + \frac{4}{3}) = 3(\frac{4}{3}) = 4\]Therefore, \(3(x+y) = 4\).