System of Equations All Methods

What is the substitution method used for in solving a system of equations?

• To solve a system of equations

• To write a novel

• To calculate the area of a circle

• To bake a cake

In the elimination method, what operation is used to eliminate one of the variables?

• Multiplication

• Addition or subtraction

• Division

• Exponentiation

How is the solution to a system of equations found using the graphical method?

• By identifying the point of intersection of the two equations on the graph.

• By adding the two equations together

• By multiplying the two equations

• By finding the average of the two equations

When is the substitution method most useful in solving a system of equations?

• When both equations are already solved

• When the equations are not related

• When the variables are not known

• When one of the equations can be easily solved for one variable

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Two linear equations with the same set of variables

• system of equations

• function

• association

• correlation

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

What are the steps involved in solving a system of equations using the elimination method?

• Identifying the variable to eliminate, multiplying the equations by appropriate constants, and adding or subtracting the equations to eliminate the variable.

• Dividing the equations by random numbers

• Ignoring one of the equations

• Solving for the variable with no elimination

Explain the concept of intersection point in the context of the graphical method for solving a system of equations.

• The intersection point represents the solution to the system of equations.

• The intersection point is the average of the two equations' slopes.

• The intersection point is the y-intercept of the first equation.

• The intersection point is the maximum value of the system of equations.