Mathematics 2016 JAMB Past Questions - Question 42: Solve for x and y respectively .3x-5y=96x-4y=12

Correct Answer

C

Explanation

3x - 5y = 9 ....................... (1)6x - 4y = 12 .......................(2)6x (1) 18x -30y = 54 ..............(3)3X (2) 18X - 12Y = 36 = ...........(4)(3) - (4) -18Y = 18y == -1substitue -1 for y in (1) to find x 3x - 5 (1)=9find x : 3x -5 (-1) = 9 3x +5 = 9 3x = 9 - 5 -= 4x = Hence, x = y = -1To solve the system of equations 3x - 5y = 9 and 6x - 4y = 12, we can use the method of substitution or elimination.Let's use the method of elimination. First, we can multiply the second equation by 3 to make the coefficients of x in both equations equal:\[9x - 15y = 27\]\[6x - 4y = 12\]Now, we can subtract the second equation from the first:\[9x - 15y - (6x - 4y) = 27 - 12\]\[3x - 11y = 15\]Now we have a new equation:\[3x - 11y = 15\]We can solve this equation for x in terms of y:\[3x = 11y + 15\]\[x = \frac{11y}{3} + 5\]Now we can substitute this expression for x into one of the original equations. Let's use the second equation:\[6x - 4y = 12\]\[6(\frac{11y}{3} + 5) - 4y = 12\]\[22y + 30 - 4y = 12\]\[18y + 30 = 12\]\[18y = 12 - 30\]\[18y = -18\]\[y = -1\]Now that we have found the value of y, we can substitute it back into the expression for x:\[x = \frac{11(-1)}{3} + 5\]\[x = -\frac{11}{3} + 5\]\[x = -\frac{11}{3} + \frac{15}{3}\]\[x = \frac{4}{3}\]So, the solution to the system of equations is \(x = \frac{4}{3}\) and \(y = -1\).