Solving Systems of Equations

This video tutorial covers solving systems of equations using various methods: elimination, substitution, and graphing. It includes examples with two variables and extends to systems with three variables. The tutorial also addresses solving word problems, providing a comprehensive understanding of these mathematical concepts.

What is the first step in solving the system of equations 2x + y = 4 and 2x - y = 0 using the elimination method?

• Divide both equations by 2

• Subtract the second equation from the first

• Add the equations to eliminate y

• Multiply both equations by 2

When solving equations with fractions, what is the recommended first step?

• Add the fractions directly

• Subtract the fractions

• Convert fractions to decimals

• Multiply by the least common multiple to clear fractions

In the substitution method, if y = 2x - 5 and y = 5x - 11, what should you do first?

• Add the two equations

• Replace y in one equation with the expression from the other

• Multiply both equations by 2

• Graph the equations

What is the solution to the system of equations y = -2x + 7 and y = 3x - 3 when solved by graphing?

• (0, 7)

• (3, 2)

• (2, 3)

• (1, 4)

When graphing the equation y = 1/3x - 2, what is the y-intercept?

• -2

• 0

• 3

• 1/3

In a system of three variables, what is a common strategy to start solving the equations?

• Add all three equations together

• Eliminate one variable using two equations

• Convert to decimals

• Graph all three equations

For the system x + y + z = 6, x + y - z = 0, and x - y + 2z = 5, what is the value of x?

• 4

• 1

• 2

• 3

If the sum of two numbers is 26 and their difference is 6, what are the numbers?

• 11 and 15

• 13 and 13

• 12 and 14

• 10 and 16

Sally invested $17,000 in two accounts with 12% and 16% interest, earning $2,400 in total. How much was in the 16% account?

• $7,000

• $10,000

• $9,000

• $8,000

In a jar with 38 coins worth $5.70, there are two more dimes than nickels. How many quarters are there?

• 14

• 16

• 12

• 10