Notes on Elimination System of Equations

Notes Elimination System of Equation

3 ways to solve Systems of Equations

1. Graphing

2. Substitution

3. Elimination

Graphing

1. When two lines intersect the intersection (x,y) is the solution

2. Parallel lines do not ever touch, they have no solution

3. Coinciding lines (one on top of other) have infinite solutions.

Multiple Choice

How many solutions?

• One Solution

• No solution

• Infinitely Many Solutions

Multiple Choice

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

Multiple Choice

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Substitution

Multiple Choice

Solve the following systems of equations using substitution:

x = 6

y = 2x - 3

• (6, 6)

• (6, 9)

• (9, 6)

• (9, 9)

Multiple Choice

Solve the following systems of equations using substitution:

y = 8

y = -4x + 4

• (8, -1)

• (-28, 8)

• (-1, 8)

• (8, -28)

-2x + 3y = 5

2x + 3y = 5

Elimination

Notice that the terms with x variables are opposites. We call this a zero pair because if we add the two equations we have zero x.

Zero pair eliminates variable

Now that one variable is eliminated we can solve for the other variable(y).

Multiple Choice

What variable creates a zero pair?

x + 3y = 18

–x –4y = –25

• x

• y

Multiple Choice

Solve the system of Equation (x,y)
3x + y = –14
–2x – y = 9

• (-5,1)
• (5,-1)
• (1,4)
• (-1,4)

Multiple Choice

Which variable creates a zero pair?

3x + y = –14

–2x – y = 9

• x

• y

Solve for (x,y)

1. Eliminate one variable using zero pair

2. Solve remaining variable

3. Substitute known variable into original equation to get both variables

Multiple Choice

-4x-2y=-12

4x+8y=-24

• (5,6)

• (6,-6)

• (6,-2)

• (4,-3)

Multiple Choice

Solve the system of Equation (x,y)

x + 3y = 18

–x –4y = –25

• (3,7)

• (-3,7)

• (7,-3)

• (-3,-7)

Multiple Choice

Solve the system of Equation (x,y)

3x + y = –14

–2x – y = 9

• (-5,1)

• (5,-1)

• (1,4)

• (-1,4)

Multiple Choice

Solve the system of Equation (x,y)

3x + y = –14

–2x – y = 9

• (-5,1)

• (5,-1)

• (1,4)

• (-1,4)

Multiple Choice

−4x − 4y = 0

4x + 4y = 0

• (−6, −4)

• Infinite number of solutions

• (−6, 10)

• (6, 4)