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Lesson 2: Systems of equations with graphing

# Systems of equations with graphing

When solving systems of linear equations, one method is to graph both equations on the same coordinate plane. The intersection of the two lines represents a solution that satisfies both equations. Other, more mathematical, methods may also be used. Created by Sal Khan.

## Want to join the conversation?

• how do you have a graph without lines
• if the number before x is positive than the line looks like this /. If the number is negative, then the line looks like this\
• Am I the only one studying in the summer
• no i am too. im scared im gonna lose all my knowledge like in previous years.
• most voted comment?
• This: if the Variable (x) is by itself, there is always a 1 in front of it. They have 115 votes
• How do you graph an equation when all it gives you is y=7
• When y equals one value
y = 7
It is a ↔️ Horizontal line, it has a Slope of Zero , it includes all x values in its solution set, but only one y…
y = 7 the seven in this case

When x equals one value
x = 2
It's a ↕️ Vertical Line, it has an Undefined Slope, it includes all y values, but only one x…
x = 2 the two in this case.

(≧▽≦) Hope this helps!
• I'm sooooo confused, I started this section after completing the last section of graphing and I 've never seen any of this before. Can some one tell me what section I need to do do be up to speed. This is the first I'm hearing of "slope intercept"......
• If you have never heard of slope-intercept form, type "slope-intercept form" at the search bar at the top of the Khan Academy homepage. Slope-intercept form is easy though. The equation for slope-intercept form is:
``y=mx+b``

In this equation, 'm' is the slope and 'b' is the y-intercept. To graph a line from a slope-intercept equation, take the value of the slope and put it over 1. For example, if the slope was 5, the slope would be 5/1. Next graph the y-intercept, take the number that is the y-intercept, and graph that number on the graph. For example, if the y-intercept was 2 graph the number 2 on the y axis of the graph. Next, take the slope, in this case 5/1, and graph it on the coordinate plane. The slope equals:
``y/x``

This is also rise divided by run. Move five places up (the rise), and one place to the left (the run). After the two points have been plotted, use a ruler to connect the two points. Now you have the line! I hope this helped!

Have a Happy New Year!
• Is anyone else still in school? (Besides me)
• Nah my school ended a month ago
• How do you know when you have to graph the line left or right?
• The video shows graphing positive and negative sloped lines, and finding their intersection…

★Both Positive and Negative lines run from Left to Right.
(all linear equations do, except Vertical)

↗️ Positive Sloped lines move upward as they move Right, increasing x-inputs = increasing y-outputs.

↘️ Negative Sloped equations move downward as the move Right, increasing x-inputs = decreasing y-outputs.

★Slope Intercept Form
y = mx + b←positive slope
y = -mx + b←negative slope

If there is a negative sign infront of the coefficient for x, (the 'm'), then the ↘️ Slope is Negative, and the line will graph from left to right, downward.

★Any two linear equations with different slope values will intersect, if on the same plane, even if they are both positive, or both negative.

(≧▽≦) I hope this helps!
• how would you graph linear systems with fractions?
• slope is very easy!
• When there is no coefficient attached to the variable (x or y), do you just assume it's equal to 1 for the rise/run?
• Whoops never mind I just saw a comment answering that question, and for those who're wondering, the answer is yes.