8th grade Algebra: Linear Systems D:'

[Carbunkel]

Normally, I do not have problems when it comes to Algebra; however this certain problem has been driving me in circles.

I had to graph two linear equations, and then find their solutions. Sure, I could sub. into the equations; however, it is required I graph, unfortunetly. -__-

Any how, the equations are x+y=-6 and 2x-y=3.

So first, I had subtracted x from the equation x+y=-6, and came to the conclusion of y=-x-6 . For 2x-y=3, I subtracted 2x (which became, -y=-2x+3) and then divided everything by -1, giving me y=2x-3.

When I graphed, my solution came out to be (0,-6), which doesn't make any sense when I sub. back into it.

Any thoughts?

 

[tkhunny]

Well, that's easy. You drew at least one of the lines wrong. Fix it. The first one goes through (0,-6), but the second one doesn't. Id start with repairing the second.

 

[Mrspi]

I had to graph two linear equations, and then find their solutions. Sure, I could sub. into the equations; however, it is required I graph.... the equations are x+y=-6 and 2x-y=3.

So first, I had subtracted x from the equation x+y=-6, and came to the conclusion of y=-x-6 . For 2x-y=3, I subtracted 2x (which became, -y=-2x+3) and then divided everything by -1, giving me y=2x-3.

When I graphed, my solution came out to be (0,-6), which doesn't make any sense when I sub. back into it.

Any thoughts?

Well.....

y =-x - 6 is correct.

This is a line with slope -1 and y-intercept -6. Start by putting a dot at -6 on the y-axis (this is the y-intercept). Next, note that the slope is -1. So, you can find another point on the line by starting at the dot you made on the y-axis, and then moving 1 unit down and 1 unit to the right. Make another dot here (1, -7). You can repeat this procedure to find other points on the line....(2, -8), (3, -9), etc. Draw the line through these points.

The second equation is
2x - y= 3
-y = -2x + 3
y = 2x - 3

To graph this line, start by making a dot at -3 on the y-axis (this is the y-intercept). The slope is 2. From the point at (0, -3), move UP 2 units and to the right 1 unit, and make another dot at (1, -1). Repeat this process...move up 2 and to the right 1, and make another dot. This one should be at (2, 1). Draw the line through these points.

Now, if you made an accurate graph, you should see that the lines intersect at (-1, -5).

Check. If x = -1, and y = -5, are the two original equations true?

First equation:
x + y = -6
(-1) + (-5) = -6
-6 = -6
True

Second equation:
2x - y = 3
2(-1) - (-5) = 3
-2 + 5 = 3
3 = 3
True.

So, it appears that the solution MUST be (-1, -5)

I hope this helps you.

 

[Carbunkel]

Thank you! Computation errors always get me, as well as do graphing errors.

Your reply was very helpful. After I read your advice, I was able to do the problem next to this one in the book.