Solving Systems of Equations

This video tutorial demonstrates how to solve a system of equations using a graphing calculator. It begins by explaining the concept of solving systems graphically and then shows how to rearrange equations into slope-intercept form. The tutorial guides viewers through graphing the equations on a calculator, finding the point of intersection, and verifying the solution algebraically. The example used is a special case where both lines share the same y-intercept, making the solution straightforward. The tutorial concludes with a verification of the solution to ensure accuracy.

What is the first step in solving a system of equations using a graphing calculator?

• Use the calculator's solve function.

• Find the x-intercepts.

• Solve each equation for y.

• Graph the equations directly.

When solving the equation 3x + 2y = 6 for y, what operation is performed first?

• Divide both sides by 3.

• Subtract 3x from both sides.

• Multiply both sides by 2.

• Add 3x to both sides.

After isolating the y term in the equation 3x + 2y = 6, what is the next step?

• Multiply by 2.

• Add 6.

• Subtract 6.

• Divide by 2.

In solving x - 2y = -6 for y, what is the first operation performed?

• Multiply by -2.

• Add x to both sides.

• Divide by -2.

• Subtract x from both sides.

What is the slope of the line represented by the equation y = -3/2x + 3?

• -3/2

• 3/2

• 1/2

• -1/2

What is the y-intercept of the line y = 1/2x + 3?

• 1/2

• 3

• 0

• -3

How do you determine the point of intersection on a graphing calculator?

• Use the calculate intersection function.

• Use the trace function.

• Use the zoom function.

• Use the graph function.

What is the ordered pair that represents the solution to the system of equations?

• (0, 0)

• (3, 3)

• (0, 3)

• (3, 0)

How can you verify that an ordered pair is a solution to a system of equations?

• By graphing the equations.

• By substituting the values into the original equations.

• By using the calculator's solve function.

• By finding the x-intercepts.

What is the result of substituting x = 0 and y = 3 into the equation 3x + 2y = 6?

• 0 = 6

• 9 = 6

• 6 = 6

• 3 = 6