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# graph and solve x+y=3 and x-y=5 using algebra

Must graph x+y=3 and x-y=5 using y=mx+b and algebra to find the x and y. Please help I'm SSOOO frustrated!

When an equation in first degree is given in the form y=mx+b then this can immediately be graphed with a slope of m and y intercept of b.  A first degree equation is an equation that does not contain any variables raised to second power or greater.

The given equation is x+y=3.  Subtract x from both sides.  This will result in the equation below:

y=3-x

Rearranging the right side we can write the above equation as

y=-x+3

This equation is of the form y=mx+b (with m=-1 and b=3)

To graph this line, mark the first point at 3 on the y axis (b is 3 from above)

Since m, which is the slope, is -1, mark another point relative to this first point 1 unit to left and 1 unit up.  We do this because the slope is -1 and a slope of -1 means 1 unit rise for -1 unit for run.

Join the two plotted points and extend in both ends to get the required line on the graph.

Do similar operations on x-y=5 as I explained for x+y=3. Perform operations on the given equation so that the equation transforms to y=mx+b form as follows:

x-y=5

subtracting y and 5 from both sides we get

x-5 = y or y=x-5

This can also be written as y=1*x-5

This is now in the form y=mx+b where m=1 and b=-5

Now mark the point -5 on the y axis. Mark another point 1 unit to the right and 1 unit up from this first point.

Join the two points and extend in both directions to get the required graph

The line for x+y=3 and x-y=5 will intersect at some point.  Note the x and y coordinates at this point of intersection.  This is the ordered pair for the required solution.

But there's also another one x-y=5 I don't know what to do with that one. Its in the same problem and I'm  suppose to put it together with x+y=3...?
Do similar operations on x-y=5 as I explained for x+y=3.  Perform operations on the given equation so that the equation transforms to y=mx+b form as follows:

x-y=5

subtracting y and 5 from both sides we get

x-5 = y or y=x-5

This can also be written as y=1*x-5

This is now in the form y=mx+b where m=1 and b=-5

Now mark the point -5 on the y axis.  Mark another point 1 unit to the right and 1 unit up from this first point.

Join the two points and extend in both directions to get the required graph