Solving Systems of Equations with Elimination

In order to solve a system of equations, both equations must be in what form?

• Slope-intercept form

  y = mx + b

• Point -Slope form

  (y - y) = m (x - x)

• Standard form

  Ax + By = C

• The form doesn't matter

In order to eliminate.......

• The x's or the y's have to have the same coefficient, with the same sign

• The x's or the y's have to have the same coefficient, with opposite signs

• It doesn't matter, we can eliminate no matter what

• One of the x's or the y's has to be a bigger number than the other one.

In this system of equations, can we eliminate without having to change anything first?

7x + 2y = 10

-7x + y = -16

• yes

• no

In this system of equations, what would be the first step?

5x + 7y = 77

5 x + 3y = 53

• Eliminate the x's

• Eliminate the y's

• Multiply the bottom row by -1 in order to eliminate the x's

• Multiply both rows by -1 in order to eliminate the x's

If I solve a system of equations, and the answer at the end is 0=2, what is the solution?

• 2

• Infinite solutions

• 0

• No solution

If I solve a system of equations, and the answer at the end is 2 = 2, what is the solution?

• 2

• Infinite solutions

• No solution

• 0

Solve this system to find the y

-4x - 3y = -15

4x -7y = -15

• y = -3

• y = 7.5

• y = 3

• y= -7.5

Solve this system for both x and y

4x + 8y = 20

-4x + 2y = -30

• (-7, 1)

• (2, -5)

• (-2, 5)

• (7, -1)

What would be the first step to solve this system?

2x + 5y = 10

x + 3y = 7

• Multiply the bottom equation by -2 in order to eliminate the x's

• Multiply the bottom equation by 2 in order to eliminate the x's

• Multiply the bottom equation by 5 in order to eliminate the y's

• Be a baby bird and expect my teacher to spoon feed me

What is the solution to this equation?

2x + 5y = 10

x + 3y = 7

• (5, 4)

• (-5, 4)

• (5, -4)

• No solution