Solving Systems of Equations by Substitution

The video tutorial explains how to solve a system of equations using substitution and graphing. It begins with a review of solving systems, then demonstrates solving one equation for y and substituting it into the other equation. The solution is verified by graphing both equations and identifying their intersection point, which represents the solution to the system.

What does solving a system of equations involve?

• Finding the x and y values that satisfy both equations

• Finding the x value that satisfies both equations

• Finding the x and y values that satisfy only one equation

• Finding the y value that satisfies both equations

What is the first step in solving the equation y - x = 5?

• Multiply both sides by x

• Divide both sides by x

• Add x to both sides

• Subtract x from both sides

After solving y - x = 5 for y, what do we substitute y with in the second equation?

• 5 - x

• x - 5

• 5 + x

• x + 5

What is the value of x when solving the equation 9x + 3(5 + x) = 15?

• 3

• 0

• 5

• 15

What is the value of y when x is found to be 0?

• 15

• 3

• 5

• 0

What is the y-intercept of the equation y = x + 5?

• 0

• x

• 1

• 5

What is the slope of the equation y = x + 5?

• 0

• 1

• x

• 5

What is the simplified form of the equation 9x + 3y = 15?

• 3x - y = 5

• x + y = 5

• x - y = 5

• 3x + y = 5

What is the slope of the equation y = -3x + 5?

• -3

• -5

• 3

• 5

Where do the two lines intersect in the graph?

• (0, 0)

• (5, 5)

• (0, 5)

• (5, 0)