Explain, in complete sentences, how you would use the graphing method to solve the following system of inequalities and what the final solution will look like on the coordinate plane.

x – 2y –8
7x + y

Question

Explain, in complete sentences, how you would use the graphing method to solve the following system of inequalities and what the final solution will look like on the coordinate plane. 

x – 2y  –8 
7x + y < –6

anonymous · Answer

@johnweldon1993 can you help with this one also? :)

johnweldon1993 · Answer

Missing the inequality sign on the 1st equation...

anonymous · Answer

x-2y(greaterthan or =to) -8

johnweldon1993 · Answer

Okay...so first step would be...solve each equation for 'y'....what equations do you get when you do that?

anonymous · Answer

y(greaterthanoreaqualto)4-x
y(lessthan)-6-7x

johnweldon1993 · Answer

$$y < -7x - 6$$ is correct

But the other one...we'll do together

$$x - 2y \ge -8$$

subtract x from both sides

$$-2y \ge -x - 8$$

divide everything by -2 ***remember when dividing by a negative number to switch the direction of the sign***

$$y \le \frac{ 1 }{ 2 }x + 4$$

understand that part?

anonymous · Answer

yess

johnweldon1993 · Answer

Okay...so now when graphing....use the fact that

$$y < -7x - 6$$

-6 is the y-intercept and -7 is the slope

and

$$y \le \frac{ 1 }{ 2 }x + 4$$

4 is the y-intercept and 1/2 is the slope

anonymous · Answer

okay and thats it?

johnweldon1993 · Answer

Almost....you graph those lines....then you need to figure out where the solutions lie....

notice the *less than* and *less than or equal to* signs

This means you would shade BELOW the lines...and where the 2 shades overlap...are your possible answers

johnweldon1993 · Answer

I'll give you an example for this problem...

johnweldon1993 · Answer

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