Question

Which graph represents the solution set of the system of inequalities? −3x+y>1 y≥x−1

Answer 1

Answer:

Option D is the correct choice.

Step-by-step explanation:

We have been given a system of inequalities. We are asked to choose the graph that represents solution set of the given system.

$-3x+y>1$

$y\geq x-1$

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

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

$y\geq x-1$

$0\geq 0-1$

$0\geq -1$

Point (0,0) satisfies inequality $y\geq x-1$, so shaded region will be area including point (0,0)

$-3(0)+0>1$

$0+0>1$

$0>1$

Point (0,0) doesn't satisfy inequality $-3x+y>1$, so shaded region will be area excluding point (0,0).

The solution set of given system of inequalities will be area of included in both inequalities.

We can see that last option is the correct choice as it has one dotted line (y-intercept 1) and one solid line (y-intercept -1).

Therefore, option D is the correct choice.

Answer 2

I think the answer will be d