Understanding Systems of Linear Equations

What is a system of linear equations?

• A single equation with multiple variables

• A set of equations with different variables

• Multiple equations with the same variable

• A single equation with one variable

What does it mean when two lines on a graph intersect at a single point?

• There is no solution

• There is one solution

• There are infinite solutions

• The lines are parallel

What is the result when two lines have the same slope but different y-intercepts?

• They intersect at one point

• They are the same line

• They are parallel and never intersect

• They form a right angle

In the substitution method, what is the first step?

• Multiply the equations by a constant

• Solve for one variable in one equation

• Graph the equations

• Add the equations together

What is the solution to the system of equations using substitution if x = -3 and y = -9?

• (-9, -3)

• (3, 9)

• (-3, -9)

• (9, 3)

What is the elimination method primarily used for?

• Finding the slope of a line

• Substituting variables

• Eliminating variables to solve systems

• Graphing equations

In the elimination method, what happens when you add two equations and one variable cancels out?

• You solve for the remaining variable

• You graph the equations

• You substitute the variable back

• You find the slope

What is the solution to the system of equations using elimination if x = 9 and y = -2?

• (9, -2)

• (-9, 2)

• (2, -9)

• (-2, 9)

What adjustment is made in the advanced elimination example to facilitate solving?

• Dividing both equations by a constant

• Adding a constant to both equations

• Multiplying one equation by a constant

• Subtracting one equation from the other

What is the solution to the system of equations in the advanced elimination example if x = 2 and y = 5?

• (-5, -2)

• (5, 2)

• (-2, -5)

• (2, 5)