Solving Systems of Linear Equations: Graphing, Substitution, and Elimination

What does the Y-intercept of a line represent in its equation?

• The point where the line crosses the Y-axis

• The slope of the line

• The X-intercept of the line

• The maximum value of the function

How is the slope of a line used when graphing?

• To find the X-intercept

• To determine the width of the line

• To calculate the area under the curve

• To plot additional points using rise over run

What does the point of intersection between two lines represent?

• A solution that satisfies both equations

• The sum of their Y-intercepts

• The midpoint of the two lines

• The point where their slopes are equal

In the substitution method, what is the first step?

• Multiply both equations by a constant

• Graph both equations

• Isolate one variable

• Eliminate one variable

What is the result of substituting one equation into another in the substitution method?

• A new equation with two variables

• An equation with no variables

• An equation with one variable

• A quadratic equation

When using the substitution method, after finding the value of one variable, what should you do next?

• Check the solution in the original equations

• Solve for the other variable using the same method

• Graph the solution on a coordinate plane

• Substitute it back into both original equations

What is the goal of the elimination method in solving systems of equations?

• To graph the equations

• To eliminate one variable

• To substitute one equation into another

• To find the Y-intercept

How do you manipulate equations in the elimination method to eliminate a variable?

• By adding the equations together

• By subtracting one equation from the other

• By multiplying the equations by coefficients that make one variable cancel out

• By dividing one equation by the other

After eliminating one variable using the elimination method, what is the next step?

• Eliminate the other variable

• Substitute the solution back into the original equations

• Solve the resulting single-variable equation

• Graph the resulting equation

What verifies that a solution is correct in both the substitution and elimination methods?

• The solution equals the sum of the Y-intercepts

• The solution is a prime number

• The solution results in a straight line

• The solution makes both original equations true