Steps to Solving Systems of Equations

What is the first step in solving a system by graphing?

• Write both linear equations in slope-intercept form

• Get x by itself

• Compare the slopes of both equations

• Write both equations in standard form

The solution to a system of equations is any ordered pair that makes both equations true.

• TRUE

• FALSE

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

The solution (x, y) to a system of equations is the point where they...?

• Run off the graph

• Don't touch

• Intersect

• Exist

When you solve these equations using the elimination method, which variable will be eliminated?

• The  x

• The  y

• The  z

• The unknown

Look for ____ when determining which variable to eliminate. Select all that apply

• same coefficeints with opposite signs

• easy numbers to multiply to (common factors)

• different coefficients

• vertical alignment of like terms

To find the second variable, substitute the x or y you solved for into one of the ____.

• original equations

• one of the manipulated equations

• the top equation, always

• the bottom equation, always

Order the algorithm (steps) to elimination

• Align like terms vertically

• Determine the variable to eliminate

• multiply equation(s) to have opposite coefficients, if necessary

• add vertically

• Solve for variable

-4x - 6y = -24

4x - 7y = - 54

Let's combine (add) these 2 equations to ELIMINATE the x variable. What would our combined equations be?

• -1y = 30

• 13y = -30

• -1y = -78

• -13y = -78