Solving Systems of Equations

The video tutorial explains how to solve a system of linear equations using the elimination method. It begins by introducing the concept of elimination and demonstrates how to add equations to eliminate one variable. The tutorial covers the principles of equation manipulation, solving for x, and then substituting to find y. Finally, it verifies the solution by checking if the values satisfy both original equations.

What is the first step in using the elimination method to solve a system of equations?

• Graph the equations to find the intersection point.

• Add or subtract the equations to eliminate one variable.

• Multiply both equations by the same number.

• Divide both equations by the same number.

In the given equations, which variable is eliminated when the equations are added?

• y

• x

• Neither x nor y

• Both x and y

After adding the equations, what is the resulting equation?

• 4x = 14

• x + y = 10

• 5y = 20

• 5x = 20

What is the value of x after solving the equation 5x = 20?

• x = 4

• x = 5

• x = 3

• x = 2

Which equation is used to substitute the value of x to find y?

• x + 2y = 6

• x - y = 2

• 4x - 2y = 14

• 2x + y = 8

What is the value of y when x = 4 is substituted into the equation x + 2y = 6?

• y = 2

• y = 3

• y = 1

• y = 0

What is the solution to the system of equations?

• x = 1, y = 4

• x = 3, y = 2

• x = 2, y = 3

• x = 4, y = 1

How can you verify the solution of a system of equations?

• By checking if the solution satisfies only one equation.

• By substituting the solution into both equations.

• By graphing the equations and checking the intersection.

• By solving the equations again using a different method.

What is the result when x = 4 and y = 1 are substituted into the first equation?

• 4 + 2 = 10

• 4 + 2 = 8

• 4 + 2 = 12

• 4 + 2 = 6

What is the result when x = 4 and y = 1 are substituted into the second equation?

• 16 - 2 = 12

• 16 - 2 = 14

• 16 - 2 = 10

• 16 - 2 = 8