Question

2. Solve the following equations: (4 pts ea.) a. 5x – 2y = 15 & 3x + 2y = -7 b. 2x + 3y = 3 & - 10x + 2y = -32

Answer 1

2.a. We have 5x-2y = 15…(1) and 3x+2y = -7…(2).

On adding the two equations, we get (5x-2y )+( 3x+2y ) = 15-7 or, 8x = 8 so that x = 8/8 = 1.

Now, on substituting x = 1 in the 1^st equation, we get 5*1-2y = 15 or, 2y = 5-15 = -10. Hence y = -10/2 = -5.

We can substitute x = 1 and y = -2 in the 2^nd equation to verify the answer ( x = 1, y = -2).

b. We have 2x+3y = 3…(1) and -10x+2y = -32…(2).

On multilying both the sides of the 1^st equation by 5, we get 10x+15y = 15…(3).

On adding the 2^nd and the 3^rd equations, we get (-10x+2y)+ (10x+15y) = 15-32 or, 17y = -17 so that y = -17/17 = 1.

Now, on substituting y= -1 in the 1^st equation, we get 2x-3 = 3or, 2x = 3+3 = 6 so that x = 6/2 = 3.

We can substitute x = 3 and y = -1 in the 2^nd equation to verify the answer ( x = 3, y = -1).