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garri49 [273]
3 years ago
12

Use a separate sheet of paper to solve the system of inequalities by graphing. Use the graph to decide if the point (1, –1) is i

n the solution set of the system. Explain your answer in the box provided below. y≤-3x+3 3x+8y≥3
Mathematics
1 answer:
Lena [83]3 years ago
6 0

Answer:

The answer is no though, the point (1,-1) is below both.

Step-by-step explanation:

So the two inequalities are y≤-3x+3 and 3x+8y≥3

With inequalities you have to know a few things.  First, when you graph you may have to use non solid lines.  for instance, if you had x<5, 5 would not be part of the answer because it is only answers less than 5.  so you represent this by making a dashed line that says "you cannot include values on this line".  Second, with algebra, if you multiply both sides by a negative it flips the inequality.  for instance -y > 54 you would multiply (or divide) by -1 and it would change to y < -54.  Third, when graphing an inequality, treat it like an equation and graph the line as if it were said equation(with solid or dashed lines as needed)  then, if it is y > f(x) you shade in the section above the line and y < f(x) shades in below.  The shaded part is your answer basically.  Now lets get into yours.

y≤-3x+3

It is already in the form y = f(x)  so grapht he line 3x + 3 with a solid line since it is y is less than or equal to,  then shade below that line.  

3x+8y≥3

First get it so y is by itself

3x+8y≥3

8y≥3 - 3x

y ≥ 3/8 - 3/8 x

Now grapht his line  with a solid line and shade the area above it.

Now, the shaded area below between y ≥ 3/8 - 3/8 x and  y≤-3x+3 and the lines are your answer, so you need to check if the point (1, -1) is in this shared shaded area or on one of the lines.

The answer is no though, the point (1,-1) is below both.

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