jfloyd1

2x + 4y = -8
y = 5x + 9

2x +4(5x + 9)= -8

2x +20X + 36= -8
22X + 36 = -8
22X = -44
x = -2

y = 5x + 9

y = 5(-2) + 9
y = -10 + 9
y = -1

The second equation is already solved for "y"
So take the value for "y" given in the second
equation and replace the "y" in the first equation.

This is what the equation should look like after replacing
the "y" with the value from the second equation. Now
solve for "x" like a regular one-variable equation.

Distribute
Add like terms
Use Addition Property (-8 - 36)
Use Division Property (-44 / 22)

Now go back to one of the ORIGINAL problems and
insert the value for "x" into the equation. Solve for "y".

The complete answer (the point of intersection) for the 2
linear equations is (-2,-1)

x - y = 7
x + y = 3

2x = 10
x = 5

5 - y = 7
5 = 7 + y
5 - 7 = y
y = -2

In using the elimination method to solve a problem you
want to make sure that one of the variables cancels out of
the equations such as the equation to the left.

To solve the system, the "y's" cancel eachother out and you
are left with the equation to the left.

By using division you will solve the problem for "x''.

Now, take the solution for "x" and put it back into one of the
ORIGINAL problems, and solve for "y".

The solution to the problem is (5,-2).

4x - y = 5
3y - 3x = 3

y = 4x - 5
y = (1)x + 1

y = 4x - 5
y = x + 1

To graph the equations to find the solution, you have two
choices : 1. Graph by hand 2. Graph using the calculator

Either way you choose, the graph should turn out as the
picture below.

First, you must the equations in "y = mx + b" format. "M"
represents the slope of the line, and "B" represents the
y intercept.

The equations should now look like this. ( All of the numbers
were divided by 3 in the second equation because you are
solving for 1 "y".) The slope ,"m", is indicated in red, and the
y intercept, "b" is indicated in blue. *** In the second equation
there is an understood "1" as the slope of the line when "x" is
alone.

Now, these two lines can be graphed by using the slope and the
y- intercept. Find where (0,-5) and (0,1) are on the graph and
plot those two points.
The slope for the first line is 4. So, from the point (0,-5) count up
4 lines on the graph and move over to the right one line, and
graph that point. Now draw a line connecting the two points
(0,-5) and (1,-1).
The slope for the second line is 1. So, from the point (0,1) count
up 1 line and over one line, and graph that point. Now draw a line
connecting (0,1) and (1,2).

Here is what the graph should look like: