Solving Systems of Equations: Graphing, Substitution, and Elimination

This video tutorial explains how to solve systems of equations using three methods: graphing, substitution, and elimination. It begins with an introduction to the topic, followed by detailed steps for each method. The graphing method involves rewriting equations in slope-intercept form and plotting them. The substitution method requires solving for one variable and substituting it into the other equation. The elimination method involves aligning coefficients to eliminate a variable. The video concludes with a summary and a call to action to like and subscribe for more math content.

What is the first step in solving systems of equations by graphing?

• Solve for x

• Plot the y-intercept

• Choose a variable to eliminate

• Rewrite the equation in slope-intercept form

What does the slope of a line tell us?

• The exact point where two lines intersect

• The x-intercept

• The y-intercept

• The direction and steepness of the line

How do you find the solution to a system of equations using graphing?

• By finding the y-intercept

• By solving for x first

• By identifying where the lines intersect

• By subtracting the equations

What is the first step in the substitution method for solving systems of equations?

• Eliminate a variable

• Solve one of the equations for one variable

• Graph the equations

• Multiply both sides of an equation

After substituting the expression into the other equation, what should you do next?

• Rewrite the equation in slope-intercept form

• Choose another variable to eliminate

• Simplify and solve for the variable

• Graph the equation

In the elimination method, what is the goal of manipulating the equations?

• To solve for one variable directly

• To make the coefficients of one variable the same

• To find the y-intercept

• To graph them more easily

What happens to the variable you choose to eliminate in the elimination method?

• It becomes the solution

• It is divided by a coefficient

• It is eliminated from the equation

• It is subtracted from the other variable

What do you do after eliminating a variable in the elimination method?

• Substitute back into the original equation

• Solve for the remaining variable

• Graph the remaining equation

• Rewrite the equations

What is the final step in the elimination method?

• Plug the found value into one of the original equations

• Eliminate another variable

• Graph the equations

• Solve for the y-intercept

What is a common result in all three methods discussed for solving systems of equations?

• The solution is x = 2 and y = 2

• A variable is eliminated

• The equations are graphed

• The slope-intercept form is used