Question

What is the value of the x variable in the solution to the following system of equations?
2x + 3y = 4
x - 2y = -5

Answer 1

Q1 : x - 2y = -5 => 2y = x +5 => y = (x+5)/2
Q2 : 2x + 3(y) = 4

Put Q1 into Q2 => 2x + 3*[(x+5)/2] = 4
times 2 to both sides ==> 2 * [2x + 3((x+5)/2)] = (4) * 2

=> 4x + 3(x+5) = 8
=> 4x + 3x +15 = 8
=> 7x = 8-15
=> x = -7/7
=> x = -1

verification if x = -1
Q1 : (-1) -2y = -5 => 4 = 2y => y = 2
Q2 : 2(-1) + 3(2) = 4 => -2 +6 = 4 ==> correct !