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Question 1204488: Solve the following system of equations graphically on the set of axes below.
y=x+8
y=−2x−4
Found 3 solutions by Alan3354, josgarithmetic, math_tutor2020:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Solve the following system of equations graphically on the set of axes below.
y=x+8
y=−2x−4
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They're 2 straight lines.
y=x+8
Pick 2 values for x and find y.
Plot the 2 points.
Draw a line thru them.
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Do the same for the 2nd equation.
The intersection is the solution of the system.
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DL the FREE software at www.padowan.dk
Use Insert, then x+8
Answer by josgarithmetic(39617)  (Show Source):
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
If your teacher allows technology to graph, there are many options to pick from. My top two favorites are Desmos and GeoGebra.
If you are in an exam setting, then use of a TI83 or TI84 or similar is probably the better route.
Here's the Desmos link to the interactive graph
https://www.desmos.com/calculator/wcygja34rd
While using tech is fine for a quick solution, it doesn't help show how the graphing process works.
The next section will cover this.
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Each equation given to us is linear because they fit the slope intercept form y = mx+b
All we need at minimum are two points to plot a line.
Each point is a pair of coordinates (x,y).
To generate any given point on the line, pick x values at random to plug into the equation to find its paired y value.
For example, let's go for x = 0
y = x+8
y = 0+8
y = 8
The input x = 0, leads to y = 8
We form the ordered pair (x,y) = (0,8)
Repeat the process with x = 1
y = x+8
y = 1+8
y = 9
The point (1,9) is also on the line y = x+8
Plot the two points (0,8) and (1,9)
Then draw a straight line through those points to finish up the graph of y = x+8
If you follow the same outline for the other equation y = -2x-4, then you should find the two points (0,-4) and (1,-6)
Let me know if you need to see the steps.
Here's what it looks like when graphing both equations on the same xy grid.
y = x+8 in green
y = -2x-4 in blue
The intersection point (-4,4) is the solution of the system.
It means x = -4 and y = 4 pair up together to make both equations true.
Let's check that claim algebraically.
y = x+8
4 = -4+8
4 = 4
The first equation has been confirmed.
Now onto the second equation.
y = -2x-4
4 = -2*(-4)-4
4 = 8-4
4 = 4
This has been confirmed as well.
Both equations have been confirmed true.
Therefore, we have confirmed the solution (-4, 4).
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