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### Course: MAP Recommended Practice>Unit 19

Lesson 27: Systems of equations with graphing

# Systems of equations with graphing: 5x+3y=7 & 3x-2y=8

To solve a system of linear equations by graphing, you need to graph each equation separately. Find two points on each line and connect them. The point where the two lines intersect is the solution to the system of equations. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Sal started with these two equations:
``5x + 3y = 7``

``3x - 2y = 8``

He didn't put them into point slope form, but played around with them and got some results. Is this called a certain form, and will this always work?
• This is called Standard form, but it is not there in the video!
• What if the two lines end up not intersecting? Are you still "solving the system using the graphing method"?
• If the lines do not intersect at all, there is no solution. If they intercept only one, there is one solution. If there seems to only be one line, there are infinite (Neverending) solutions.
• What if you get a fraction for the y-intercept when putting the equation(s) into slope-intercept form (y=mx+b)?
• There's no problem if you get a fraction for the y-intercept. For example, let's say I have a line whose slope is 2 and y-intercept is 3/5. The slope-intercept form of this line would be: y = 2x + 3/5
• what about problems that have something like y=3x?
• In such a situation, the y-intercept, and the x- intercept are both (0,0). You can tell this, because if you plug in 0 for either x or y, or get 0 for the other. EX:
y=3x → 0=3x → 0/3=x=0
In order to graph, you would draw a line extending from the origin, increasing at a rate of 3 units. Consider the video Algebra: graphing lines 1
• I'm still confused...Why did it transform into a fraction?
• Sal is solving these by finding the intercepts, intercepts always have a 0 somewhere. x intercepts have y=0 (x,0) where x is a number, and y intercepts have x=0 (0,y). Doing this, he ends up with 3y=7. To isolate the y, you have to divide both sides by 3 which ends up as a fraction y=7/3. Same thing happens with x intercept.
• So you just graph the slope?
• Yes except carry the eight on the right.
• I'll give an example.
y=6x+3
1.)The 6x is really saying its 6/1 aka...(rise over run)
2.)3 is the y-axis, so start at 3 on the y-axis.remember 3.)that its positive.
4.)Then 6/1= move 1 in the x-axis,then 6 in the y-axis,and you'll get your line.
How to convert this 4x-4y=8 into y=x-2
Lets start by moving the 4x part onto the other side of the equal sign,and we can do that by subtracting 4x from both sides.
1.)4x-4y=8
2.)-4y=8-4x
3.)y=-2+1x
4.)y=x-2