Question

X + y = 2

2x - y = 7
Which of the following ordered pairs (x, y) satisfies the system of equations above?
A. (-1,3)
B. (5,-3)
C. (3, 1)
D. (3,-1)

Answer 1

`D. (3,-1)`

Explanation:

`x + y = 2 \: \: \: \: \: \: ..(1) \\ </p><p>2x - y = 7 \: \: \: \: ..(2)`

from equation 1 we get,

`x = 2 - y`

now,

`put \: \: \: \: x = 2 - y \: \: \: in \: (2)`

we get,

`2(2 - y) - y = 7 \\ 4 - 2y - y = 7 \\ 4 - 3y = 7 \\ - 3y = 7 - 4 \\ - 3y = 3 \\ \\ y = (3)/(( - 3)) \\ \\ y = - 1`

now,

`put \: \: \: \: y = - 1 \: \: \: \: in \: (1)`

we get,

`x + ( - 1) = 2 \\ x - 1 = 2 \\ x = 2 + 1 \\ x = 3`

hence, the value of x = 3 and y = (-1)