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### Course: Digital SAT Math > Unit 2

Lesson 8: Graphs of linear systems and inequalities: foundations# Graphs of linear systems and inequalities — Harder example

Watch Sal work through a harder graphs of linear systems and inequalities problem.

## Want to join the conversation?

- Would someone show the other method of solving this problem?(16 votes)
- To find the equation of first line:

Gradient = (-2-0)/(8--2) = -0.2

y = -0.2x + c

By substituting any of the two coordinates we get

c = 0.4

So y = -0.2x - 0.4

Similarly, find the y intercept of second equation and we get:

y = -2x + 5

Solve the equations simultaneously by using elimination or substitution method to get the point of intersection.

Using substitution method:

-0.2x - 0.4 = -2x + 5

1.8x = 5.4

x = 3

y = -2(3) + 5 = -1

Lastly, add the x and y coordinates of intersection point to get the final answer.

3 + (-1) = 2(45 votes)

- but can we even use a paper to draw all that in the digital sat?(16 votes)
- You actually don't need to graph in order to solve the problem.(12 votes)

- Yeah no. It would've taken approximately the same time to use either method.(18 votes)
- How do I do the other method?(7 votes)
- get slope of first line and write in slope intercept form and plug any of the passing point to get b and make the equation. for 2nd line, plug any of the passing point to get b and make the equation as slope is already given. you will get the following equations: y=-1/5x-2/5 and y=-2x+5 and equate both of them and get the value of one than plug that value into any of the equation to get the value of another. and add both of them.(20 votes)

- this is harder than I thought(16 votes)
- Guys it’s much easier with desmos calculator(4 votes)
- While it is easier to solve the equation on a calculator, solving it without a calculator is far more beneficial to your mental strength.(2 votes)

- i solve it without graph , and its much easier(4 votes)
- Would you please share your method? I find this pretty hard with all the graphs involved.(2 votes)

- if you all find this confusing, you can find the equation of both lines and put them on Desmos(you are allowed to use Desmos throughout the entire test) and it will show the point(a,b) where they intercept for you(4 votes)
- I still didn't get how to graph the slope if it was given like the (-2)?

I just know how to graph it if he gives me two points(4 votes)