Solving Systems of Equations with Three Variables

The video tutorial covers solving a system of three equations using the elimination method, solving a word problem involving investments with different interest rates, and calculating the cost of apples and bananas using algebraic equations. Each section provides a detailed step-by-step approach to solving these problems, emphasizing the use of algebraic techniques to find solutions.

What is the first step in solving a system of three equations?

• Divide all equations by the same number.

• Subtract one equation from another.

• Choose two equations and add them to eliminate one variable.

• Multiply all equations by the same number.

After eliminating the variable y from the first two equations, what is the resulting equation?

• 4x + 3z = 13

• 3x + 2z = 6

• 5x + 3z = 14

• 2x + 3z = 7

What is the value of x after solving the system of equations?

• 0

• 2

• 3

• 1

How do you find the value of z after determining x?

• Substitute x into the original first equation.

• Substitute x into the second equation in terms of x and z.

• Substitute x into the third equation.

• Substitute x into any equation.

What is the total investment amount in the word problem involving investments?

• $13,000

• $15,000

• $19,000

• $8,000

How much money was invested in the account paying 15% interest?

• $19,000

• $13,000

• $8,000

• $5,000

What is the interest earned from the account paying 14% interest?

• $1,200

• $700

• $1,900

• $8,000

What is the cost of 5 apples and 8 bananas?

• $8.75

• $6.55

• $9.20

• $7.50

What is the cost of a single apple?

• $0.35

• $0.75

• $0.50

• $1.00

What is the total cost of 7 apples and 10 bananas?

• $7.50

• $8.75

• $9.20

• $6.55