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

Answer:

$D. (3,-1)$

Step-by-step explanation:

$x + y = 2 \: \: \: \: \: \: ..(1) \\

2x - y = 7 \: \: \: \: ..(2)$

from equation 1 we get,

$x = 2 - y$

now,

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

we get,

$2(2 - y) - y = 7 \\ 4 - 2y - y = 7 \\ 4 - 3y = 7 \\ - 3y = 7 - 4 \\ - 3y = 3 \\ \\ y = \frac{3}{( - 3)} \\ \\ y = - 1$

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)