SOLUTION: Solve the following systems graphically -x+3y=8 x+y=2

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Question 887699: Solve the following systems graphically
-x+3y=8
x+y=2
Found 2 solutions by jim_thompson5910, algebrapro18:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Graph the two equations on the same xy axis. Use a graphing calculator to get



Graph of (green) and (blue)

Use the graphs 'intersect' feature to find the two lines cross at the point (-0.5, 2.5)

This is the same as (-1/2, 5/2) after you convert those decimals to fraction form.


Final Answer: (-1/2, 5/2) which means x = -1/2, y = 5/2
Answer by algebrapro18(249)   (Show Source): You can put this solution on YOUR website!
To graph a line all you need is two points on that line. You can either pick points and plug them into the equations given or, and this is how I will do it, you can get both equations into slope intercept form which will give you the two points you need to graph each line.

So first we need to solve each equation for y to get it into slope intercept form.

-x+3y = 8 add x to both sides
3y = 8+x divide both sides by 3
y = 8/3 + 1/3x

x+y=2 subtract x from both sides
y = 2-x

Now that we have both equations in slope intercept form we can look at each equation individually. tells us that the y intercept is 8/3 and the slope is 1/3. So we know that the graph goes through the point (0,8/3) from the y-intercept. And remembering that slope is the change in y over the change in x we know that the graph then goes up one and over 3. So our new point would be (0+3,8/3+1) or (3,11/3). You can plot these two points and then connect the points with the line.

Next we look at . The y intercept is 2 and the slope is -1. So we know that the graph goes through the point (0,2) from the y-intercept. Moving down 1 and over 1 puts our next point at (0+1,2-1) or (1,1). Plotting these two points will yield your line.

To finish this problem you will look to see where the two lines intersect. This will be your solution. I will leave this for you to do.

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