Question

Which graph represents the solution to the system of inequalities?

x + y ≤ 4

y – x ≥ 1

Answer 1

ANSWER

The correct answer is C.

EXPLANATION

To find which set represents the solution set of the system of inequalities, the best thing is to graph the inequalities and locate the intersection of the solution region of the two graphs.

The given inequalities are,

$x + y \leqslant 4 \: \: and \: \: y - x \geqslant 1$

Let us start with,

$x + y \leqslant 4$

To graph this inequality, we first of all graph the corresponding linear equation,

$x + y = 4$

using the intercepts,
$(0,4) \: and \: (4,0)$

We plot the above points and draw a solid straight line through them.

We test for the origin to determine which half plane should be shaded.

$0 + 0 \leqslant 4$

$0 \leqslant 4$

This statement is true, so we shade the lower half plane.

We repeat the same process to graph,

$y - x \geqslant 1$

So we graph the corresponding straight line,

$y - x = 1$

using the intercepts,

$(0,1) \: and \: (-1,0)$

We plot the intercepts and draw a solid line through them.

We test for the origin again to see which half plane to be shaded.

$0 - 0 \geqslant 1$

$0 \geqslant 1$

This statement is false, so we shade the
upper half plane.

The intersection of the two region is the region in option C of the graphs provided.