Solving Systems of Linear Equations

This GED review video covers solving systems of linear equations using three methods: linear combination, substitution, and graphing. The video explains each method step-by-step, demonstrating how to find the solution for two equations with two variables. It also highlights the importance of understanding slope-intercept form for graphing solutions.

What is a system of linear equations?

• A single equation with one variable

• Two equations with two variables

• Three equations with three variables

• An equation with no variables

What is the first step in the linear combination method?

• Add the equations directly

• Subtract one equation from the other

• Multiply one equation by a number

• Graph the equations

In the linear combination method, what is the goal of multiplying an equation by a number?

• To make the equations identical

• To eliminate one of the variables

• To simplify the equation

• To change the slope of the line

What is the next step after finding the value of one variable in the linear combination method?

• Multiply the equations again

• Substitute the value into one of the original equations

• Check the solution in both equations

• Graph the solution

What is the result of adding two equations in the linear combination method?

• The solution to the system

• A new equation with one variable

• The slope of the lines

• A new equation with two variables

What is the purpose of multiplying an equation by a constant in the linear combination method?

• To find the y-intercept

• To simplify the equation

• To change the slope

• To eliminate a variable

What does the substitution method involve?

• Graphing both equations

• Eliminating one variable by adding equations

• Solving one equation for one variable and substituting into the other

• Multiplying both equations by a constant

What is the first step in the substitution method?

• Add the equations

• Multiply the equations by a constant

• Solve one equation for one variable

• Graph the equations

In the substitution method, what do you do after isolating one variable?

• Add the equations together

• Multiply the equation by a constant

• Substitute it into the other equation

• Graph the equation

Which method involves getting one variable by itself and substituting it into the other equation?

• Graphing

• Elimination

• Linear combination

• Substitution