Exploring Rational Expressions in Algebra

What is a system of linear equations?

• An equation with no variables

• A quadratic equation

• Two or more linear equations with two or more variables

• A single linear equation with one variable

What is the solution to a system of linear equations?

• An ordered pair where the equations intersect

• A graph

• A single number

• A matrix

In Example 1, what is the first step to check if (1, 3) is a solution?

• Find the slope

• Solve for y

• Graph the equations

• Replace x with 1 and y with 3 in the equations

In Example 1, why is (1, 3) not a solution to the system?

• Both equations are true

• One of the equations is not true

• The ordered pair is not in the correct form

• The equations do not intersect

In Example 2, what is the result of substituting x = 2 and y = -1 in the first equation?

• 2

• 4

• 6

• 0

What is the first step in solving systems by graphing?

• Substitute values

• Isolate y

• Check the solution

• Find the slope

When graphing, what does the y-intercept represent?

• The solution to the system

• The point where the line crosses the x-axis

• The point where the line crosses the y-axis

• The slope of the line

In the additional example, what is the slope of the line y = 1/3x - 3?

• 1

• 1/3

• 3

• -3

How do you check if the point of intersection is the solution?

• Graph the equations again

• Substitute the point into both equations

• Find the slope

• Isolate y

What is the solution to the system in the additional example?

• (1, 1)

• (-2, 3)

• (3, -2)

• (0, 0)