Solving Systems of Equations

This video tutorial explains how to solve systems of equations using the elimination method with multiplication. It covers scenarios where neither variable has the same coefficient, requiring multiplication of one or both equations to align coefficients. Two examples are provided: one where only one equation is multiplied and another where both are multiplied. The video concludes with a practice problem for viewers to solve.

What is the main topic discussed in this video?

• Solving systems of equations by substitution

• Solving quadratic equations

• Solving systems of equations by graphing

• Solving systems of equations by elimination with multiplication

Why might you need to multiply equations when using elimination?

• To make the equations longer

• To make the coefficients of one variable the same

• To change the variables

• To solve for a different variable

In the example given, what was the first step to solve the system 2x + y = 8 and 5x + 3y = 13?

• Add the equations directly

• Multiply the first equation by 3

• Multiply the second equation by 2

• Subtract the second equation from the first

After multiplying the first equation by 3, what is the new equation?

• 6x + 3y = 24

• 5x + 3y = 13

• 2x + y = 8

• 15x + 9y = 39

What is the result of subtracting the second equation from the modified first equation in Example 1?

• y = 5

• x = 5

• y = 11

• x = 11

In Example 1, what is the value of y after solving the system?

• 1

• 2

• 3

• 4

What is the ordered pair solution for the system in Example 1?

• (11, 1)

• (1, 11)

• (1, 3)

• (3, 1)

In Example 2, why is it necessary to multiply both equations?

• To make the equations longer

• To make the coefficients of one variable the same

• To solve for a different variable

• To change the variables

What is the new coefficient of y after multiplying the top equation by 2 and the bottom by 5 in Example 2?

• 20

• 15

• 10

• 5

What is the value of x after solving the system in Example 2?

• 5

• 6

• 7

• 8