Solving Systems of Equations

The video tutorial explains how to solve a system of equations using the substitution method. It begins by identifying the need to solve for one variable and demonstrates substituting the value of y from one equation into another. The tutorial then shows how to clear fractions by multiplying through the equation, leading to the solution for x. Finally, it calculates the value of y and presents the solution as an ordered pair.

What is the main challenge when solving a system of equations with two variables?

• You cannot solve for one variable directly.

• There are too many variables.

• The equations are too complex.

• The variables are not defined.

What is the first step in solving the system of equations in the video?

• Add the equations together.

• Multiply the equations.

• Substitute the value of y from one equation into the other.

• Divide the equations.

Why do we multiply the entire equation by two in the video?

• To simplify the addition.

• To change the variable.

• To eliminate the fractions.

• To make the equation longer.

What is the result of multiplying the equation by two?

• The variables are eliminated.

• The fractions are cleared.

• The equation becomes more complex.

• The fractions remain.

After clearing the fractions, what is the next step?

• Add more variables.

• Solve for x.

• Multiply by another number.

• Solve for y.

What value of x is found after solving the equation?

• 15

• 20

• 10

• 25

Once x is found, what is the next step?

• Solve for another variable.

• Substitute x back into the original equation to find y.

• Multiply x by another number.

• Divide x by two.

What is the value of y after substituting x back into the equation?

• 10

• 12

• 14

• 16

What is the final solution to the system of equations?

• (10, 12)

• (20, 10)

• (15, 12)

• (20, 12)

What method is primarily used in the video to solve the system of equations?

• Matrix method

• Elimination method

• Substitution method

• Graphical method