Determine graphically the solution set for the system of inequalities. 3x − 2y > −13 −x + 2y > 7

vazelinahS

vazelinahS

Answered question

2021-03-09

Determine graphically the solution set for the system of inequalities.
3x2y>13
x+2y>7

Answer & Explanation

Gennenzip

Gennenzip

Skilled2021-03-10Added 96 answers

We have been given a system of inequalities and we need to graph its solution. First of all, we will graph the two linear equations. Our system of inequalities is 3x-2y>-13 and -x+2y>7.
The corresponding linear equations are 3x-2y>-13 and -x+2y>7.
We can write these linear equations in slope intercept form as shown below:
3x2y13yy<32x+132
x+2y>7y>12x+72
Now, we graph the two equations using the slope and y intercept as shown on below link:
image
Finally, we shade the region based on origin testing.
First inequality: 3(0)-2(0)>-13 gives us 0>-13, which is a true statement, so we shade the region containing origin.(DARK GREEN)
Second inequality -0+2(0)>7 gives us 0>7 which is a false statement, so we shade the region without origin
Thus, we get the required graph as:
image

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