How to Use One Multiplier to Solve a System of Equations by Elimination

The video tutorial explains solving equations using substitution and elimination methods. It highlights the challenges of substitution, especially with fractions, and introduces elimination as an alternative. The tutorial details steps for aligning variables and using multipliers in elimination, and demonstrates solving equations to identify cases with no solutions, such as parallel lines.

What is a common challenge when using substitution to solve equations?

• It always results in fractions.

• It requires solving for a variable with a non-unit coefficient.

• It is only applicable to linear equations.

• It cannot be used with negative numbers.

Why might substitution not be the best method for solving certain equations?

• It requires graphing the equations.

• It can lead to complex fractions.

• It is too time-consuming.

• It only works for quadratic equations.

What is the first step in the elimination method?

• Find the least common multiple.

• Graph the equations.

• Align the variables in each equation.

• Solve for one variable.

How do you achieve common coefficients in the elimination method?

• By subtracting the equations.

• By using multipliers on the equations.

• By adding a constant to each equation.

• By dividing each term by the same number.

In the context of elimination, what is the significance of having a zero coefficient for a variable?

• It eliminates the variable from the equation.

• It indicates a solution has been found.

• It means the variable is undefined.

• It suggests the variable is a constant.

What does it mean if the elimination method results in a false statement like 0 = 17?

• The equations have no solution and are parallel.

• The equations are inconsistent.

• The equations have infinite solutions.

• The equations are dependent.

What type of lines represent equations with no solution?

• Parallel lines

• Coinciding lines

• Intersecting lines

• Perpendicular lines