Solving Systems of Equations: Elimination and Substitution Techniques

The video tutorial explains how to solve systems of equations using two methods: elimination and substitution. It begins with an introduction to the elimination method, demonstrating how to add equations to eliminate variables and solve for the remaining ones. Two examples are provided to illustrate this method. The tutorial then transitions to the substitution method, explaining how to substitute one equation into another to find solutions. Again, examples are used to clarify the process. The video aims to equip viewers with the skills to solve systems of equations using these two techniques.

What is the first step in solving equations using the elimination method?

• Multiply one equation to make coefficients match

• Add the two equations directly

• Divide one equation by the other

• Substitute one variable from one equation into the other

What is the result of adding the two equations in the first elimination example?

• 2x plus 5x equals 7x

• x equals 1

• y equals 2

• 7x equals 7

After modifying the second equation in the second example, what is the next step?

• Subtract one equation from the other

• Divide both sides by the coefficient of y

• Add the modified equations together

• Substitute the value of x into the first equation

In the second elimination example, why do we multiply the second equation by -2?

• To simplify the equation

• To prepare the equations for addition

• To make the coefficient of x in both equations equal

• To eliminate the variable y

In the first substitution example, what do you substitute into the second equation?

• The coefficient of x

• The expression for y from the first equation

• The value of x from the first equation

• The sum of the two equations

In the first substitution example, what operation do we perform after distributing the 3?

• Combine like terms

• Add the two equations

• Substitute the value of x

• Multiply both sides by 3

How do you find the value of x in the second substitution example?

• By substituting y with its expression in one of the equations

• By dividing one equation by the other

• By multiplying the coefficients of x

• By adding the two equations

How do we solve for x in the example where y equals 3x plus 2 and y equals 7x minus 6?

• By adding 6 to both sides

• By subtracting 3x from both sides

• Both A and B

• By dividing both sides by 7

What is the final step in solving for y in the third substitution example?

• Substitute the value of x back into the original equation

• Divide both sides by the coefficient of x

• Multiply the equation by the coefficient of y

• Add the value of x to both sides of the equation

In the final substitution example, what is the value of y after substituting x = 1 into the equation for y?

• y equals 3

• y equals 5

• y equals 7

• y equals 2