Solving Systems of Equations

This video tutorial teaches how to solve systems of equations algebraically using the substitution method, particularly when one equation is in slope-intercept form. It begins with an introduction to systems of equations and the methods for solving them, focusing on substitution. The tutorial provides examples of substitution from past mathematical problems and then demonstrates solving a system step-by-step. The process includes substituting values, simplifying equations, and verifying solutions. The video concludes with a summary of the method and a check using graphing.

What is the primary focus of this lesson?

• Understanding the quadratic formula

• Graphing linear equations

• Solving quadratic equations

• Solving systems of equations by substitution

Which form is emphasized for one of the equations in this lesson?

• Point-slope form

• Quadratic form

• Standard form

• Slope-intercept form

What is the first step in substitution when given x = -8 in the equation x^2 + 9?

• Add 9 to x

• Multiply x by 2

• Divide x by 2

• Substitute -8 for x

In the equation y = 2x - 4, what is y when x = 3?

• y = 0

• y = 6

• y = 2

• y = 8

What is the first step in solving the system y = -3x + 5 and 5x - 4y = -3 by substitution?

• Multiply the equations

• Substitute y in the second equation

• Add the equations

• Graph the equations

After substituting y = -3x + 5 into 5x - 4y = -3, what is the next step?

• Divide by 4

• Use the distributive property

• Add 5 to both sides

• Subtract 3 from both sides

What is the value of x after solving 17x = 17?

• x = 1

• x = 17

• x = -1

• x = 0

How do you find y after determining x = 1 in the system?

• Substitute x into the first equation

• Use the quadratic formula

• Substitute x into the second equation

• Graph the equations

What is the solution to the system of equations?

• (3, 4)

• (2, 1)

• (1, 2)

• (0, 0)

What is the graphical representation of the solution to the system?

• The point where the lines intersect

• The point where the lines are parallel

• The point where the lines are perpendicular

• The point where the lines overlap