Mastering Systems of Equations through Graphing

What is a system of equations?

• A single equation with multiple variables

• Two or more equations that are solved together

• An equation with no variables

• A set of unrelated equations

What does it mean to solve a system of equations?

• Finding the values that make all equations in the system true

• Identifying the y-intercept of each equation

• Finding the slope of each equation

• Graphing each equation separately

In the equation y = x + 5, what is the y-intercept?

• 0

• 1

• x

• 5

How do you determine the slope of the equation y = -4x?

• By identifying the y-intercept

• By solving for y

• By finding the coefficient of x

• By graphing the equation

What is the solution to the system of equations y = x + 5 and y = -4x?

• (0, 5)

• (5, 0)

• (1, -4)

• (-1, 4)

How can you verify the solution to a system of equations?

• By calculating the slope

• By graphing the equations again

• By substituting the solution back into the original equations

• By finding the y-intercept

What is the y-intercept of the equation y = -x + 5?

• 5

• -5

• -1

• 0

How do you find the x-intercept of the equation -x + 2y = 4?

• By setting y to 0 and solving for x

• By setting x to 0 and solving for y

• By finding the slope

• By graphing the equation

What does it mean if two lines on a graph are parallel?

• They coincide

• They have the same slope but different y-intercepts

• They intersect at one point

• They have different slopes

What is the solution to a system of equations if the lines coincide?

• Two solutions

• Infinite solutions

• One solution

• No solution