System of Linear Equations

System of Linear Equations

The basic form of the equation is:

Y = MX + B, where

Y= output X = input

M = Slope B = Y intercept

If the slope is positive, the line moves from lower left to upper right

If the slope is negative, the line moves from upper left to lower right

If there is no "b", then the line passed through the origin.

Both equations need to be in the Y = MX + B form

Convert the equations to Y = MX + B form

Y - 3x = 7

Y + 2x -8 = 0

4X - y = 0

Solving a system of linear equations may be done by:

Graphing

Substitution

Elimination

To solve by graphing, there are 3 steps for each equation

Step 1: Make a chart

Step 2: Set X = 0, solve for Y

Step 3: Set X = 1, solve for Y

If the slope is a fraction, Step 3 becomes:

Step 3: Set X = to the denominator, add the numerator to B

You need 2 points to graph a line

To solve by substitution:

E=When each equation is in Y = MX + B form, Y = Y

Y =2x - 5, Y = 3x + 6

2x - 5 = 3x + 6

-2x = 2x

- 6 = -6

x = -11

Substitute -11 for X in either equation

Y = -27

to solve by elimination, look for the variable with the same coefficient

3y - 2x = 6

6y + 2x = 12

If the variables with the same coefficient are opposite signs, Add.

If the variables with the same coeffient at the same signs, subtract

In the equations above, after adding, the sum is 9y = 18

y = 2

x = 0

Solve the following systems of equations by whatever method you choose:

y = 2x + 9, y = 6 - x

y = -x - 4, y = 3/5x + 4

y = 2x + 5y, y = 1/2x -1