Question

which of the following pairs is a solution of the system of linear equations below?
$2x + y = 4$
$x - y = -1$
a $(x,y) = (1,2)$
b $(x,y) = (-3,-2)$
c $(x,y) = (2,0)$
d $(x,y) = (3,-1)$

Explanation:

Step1: Add the two equations

$$(2x + y) + (x - y) = 4 + (-1)$$
$$3x = 3$$

Step2: Solve for x

$$x = \frac{3}{3} = 1$$

Step3: Substitute x=1 into first equation

$$2(1) + y = 4$$
$$2 + y = 4$$

Step4: Solve for y

$$y = 4 - 2 = 2$$

Step5: Verify with second equation

$$1 - 2 = -1$$, which matches the second equation.

Answer:

A. $(x, y) = (1,2)$