SOLUTION: Solve by graphing. x=-y (can't figure out slope) x+y=4 Can't figure out where the two points meet.

Question 240071: Solve by graphing.
x=-y (can't figure out slope)
x+y=4
Can't figure out where the two points meet.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You really don't need to figure the slope, you just need to perform the following steps once for each of your equations.

Step 1: Select a value for

. It can be anything you want, but I suggest selecting a small integer.

Step 2: Substitute the selected value for

in the equation, and then do the arithmetic to solve the equation for

Step 3: Create an ordered pair

using the value of

you selected in Step 1 and the value of

you calculated in Step 2.

Step 4: Plot the ordered pair from Step 3 on your coordinate plane.

Step 5: Repeat Steps 1 through 4 once more using a different value for

.

Step 6: Draw a line through the two plotted points.

Once you have graphed both lines, see where they intersect. That is, if they intersect. If you end up with two separate lines that do not intersect, then your solution set is the empty set. If you end up with two lines that do intersect in one point, your solution set is the ordered pair representing that point of intersection. If you end up with one line right on top of the other, then your solution set is the set of ordered pairs that satisfies either of the two equations. Such a set has in infinite number of elements.

On the other hand, if you do feel the need to determine the slope, then solve each of the equations for

. That means do whatever is necessary (and follows the rules of algebra) to get

all by itself on the left-hand side of the equal sign and everything else on the right-hand side.

For your first one:

Rewrite it:

Multiply by -1:

Once a two variable linear equation is solved for

, then the equation is in slope-intercept form. That means that the slope is the coefficient on the

term. The coefficient on your

term is -1. Hence the slope is -1.

Do your other one the same way.

By the way: Congratulations. This is my 5000th answer on this site. You don't win anything and neither do I, but I just wanted to share.

John

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