Question

Which graph represents the solution set of the system of inequalities?

{-3x + y > 1
{y > x - 1

Answer 1

The graph that represents the solution set of the system of inequalities:

{-3x + y > 1}

{y > x - 1} is Graph D.

What is a system of inequalities?

A system of inequalities represents a set of two or more inequalities in one or more variables.

We use systems of inequalities when solving a problem with a range of solutions and there is more than one constraint.

This solution region intersects the various lines’ shadings and represents the area where all the inequalities are happy.

{-3x + y > 1}

{y > x - 1}

The boundary line of
`-3x + y > 1` is a dotted line as it has a
`>` sign. The boundary line of this inequality will cross y-axis at point (0,1) and with a slope of 3.

The boundary line of
`y \geq x - 1\\` will be a solid line as it has a
`\geq` sign. The boundary line of this inequality will cross y-axis at point (0,-1) with a slope of 1.

Now, we will check point (0,0) in both inequalities to find the shaded region.

`y \geq x - 1\\y \geq x - 1\\0 \geq > 0 - 1\\\\0 \geq -1`

Thus, the solution set of the system of inequalities {-3x + y > 1, y > x - 1} is the region of the plane where all of the individual lines’ shading overlaps, which is Option D.