Solve systems by elimination

What is the result of a system of equations if the lines are parallel?

• The system has one solution, as the lines intersect at a point.

• The system has infinitely many solutions, as the lines overlap.

• The system has no solution, as the equations represent lines that never intersect.

• The system has a unique solution, as the lines are distinct.

What is a common mistake when using the elimination method?

• Not properly aligning the coefficients or incorrectly adding/subtracting the equations.

• Using the wrong variable in the equations.

• Ignoring one of the equations completely.

• Assuming all equations are linear.

What does it mean to 'eliminate' a variable in a system of equations?

• To remove a variable from an equation without solving it.

• To manipulate the equations so that one variable is removed, allowing for the other variable to be solved directly.

• To substitute one variable with another in the equations.

• To add the equations together to find a solution.

Solve by elimination: @@-6x + 5y = 1@@ and @@6x + 4y = -10@@. What is the solution?

• (-1, -1)

• (1, 1)

• (0, 0)

• (-2, 2)

What is the first step in using the elimination method?

• To add the equations together directly.

• To manipulate the equations (if necessary) so that the coefficients of one of the variables are opposites.

• To substitute one variable into the other equation.

• To graph the equations to find the intersection point.

Given the system of equations: @@3x - 2y = 12@@ and @@2x + 2y = -2@@, which variable will eliminate when adding the equations?

• x

• y

• z

• w

What is the difference between the elimination method and substitution method?

• The elimination method solves one equation for a variable and substitutes it into the other equation, while the substitution method removes a variable by adding or subtracting equations.

• The elimination method removes a variable by adding or subtracting equations, while the substitution method solves one equation for a variable and substitutes it into the other equation.

• The elimination method is used only for linear equations, while the substitution method can be used for both linear and non-linear equations.

• The elimination method requires the equations to be in standard form, while the substitution method does not have such a requirement.

What is the graphical interpretation of solving a system of equations?

• The solution represents the point where the two lines intersect on a graph.

• The solution represents the area where the two lines are parallel.

• The solution represents the average of the two equations.

• The solution represents the distance between the two lines.

What is the importance of aligning coefficients when using the elimination method?

• Aligning coefficients allows for easy addition or subtraction of the equations to eliminate a variable.

• Aligning coefficients helps in finding the slope of the equations.

• Aligning coefficients is necessary for graphing the equations accurately.

• Aligning coefficients ensures that the equations are balanced and equal.

Solve using elimination: @@4x + 8y = 20@@ and @@-4x + 2y = -30@@. What is the solution?

• (7, -1)

• (5, 2)

• (3, 4)

• (0, 0)