Linear Systems Elimination Strategy

Which variable will be eliminated first?

• x

• y

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, how many of each type of ticket were sold? What of the following systems represent this situation?

• S + A = 530

  3S + 4A = 1740

• S + A = 530

  4S + 3A = 1740

• S + A = 1740

  3S + 4A = 530

• S + A = 1740

  4S + 3A = 530

Which method would be best (quickest) for solving the system below:

x + y = 11

3x - 4y = -2

• Making trials

• Elimination

• Graphing

• None of these

What would be the first step to solve this system by elimination?

2x+9y= -7

6x-3y= 9

• Add the equations

• Subtract the equations

• Write each equation in slope intercept form.

• Multiple the first equation by 3 or -3

To eliminate the x-variable in the system of equations, multiply the second equation by which number?

• -3

• -2

• -1

• 0

Which strategy is the best choice for solving this system?

4x − 4y = 10

4x + 4y = 0

• Elimination

• Making trials

• Substitution

• Graphing

Is the point (-2, 4) a solution to the system of equations shown below?

• yes

• no

When does a system of equations have no solutions?

• When the lines cross in only one point

• When lines are perpendicular

• When the lines are parallel

• There is ALWAYS a solution!

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines

• Same line

• Parallel lines

What would be the first step in finding the solution using elimination?

• you cannot solve this using elimination

• cross out the 2x and 3x

• Add the like terms. The y terms will cancel out.

• change to slope intercept form and graph