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

Question

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!

Answer 1

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.