Solving Systems of Equations by Linear Combination

This video tutorial teaches how to solve systems of equations using linear combination, also known as elimination. It begins with an introduction to the method, followed by a graphical approximation of the solution. The tutorial then provides a detailed algebraic solution using linear combination, emphasizing the simplicity of this method compared to substitution, especially when dealing with coefficients. The video concludes by verifying the solution through graphing and algebraic methods.

What is another name for the linear combination method?

• Substitution

• Elimination

• Graphing

• Integration

Why might substitution be complicated for the given system of equations?

• The equations involve many fractions.

• The equations have no variables.

• The equations are not in standard form.

• The equations have no solutions.

What is the approximate intersection point found by graphing the given equations?

• (2, 2)

• (0, 0)

• (-4, -4)

• (4, 4)

What is the purpose of multiplying the first equation by -3 in the linear combination method?

• To make the coefficients of x equal

• To eliminate the y variable

• To make the coefficients of y equal

• To eliminate the x variable

What property allows us to multiply an equation by a constant?

• Subtraction property of equality

• Multiplication property of equality

• Division property of equality

• Addition property of equality

After eliminating one variable, what is the next step in solving the system?

• Multiply both equations by another constant

• Graph the equations again

• Substitute the found value into one of the original equations

• Add the equations again

What is the final solution for the system of equations?

• (4, 4)

• (-4, -4)

• (2, 2)

• (0, 0)