Solving Systems of Equations Using Substitution

The video tutorial explains the substitution method for solving systems of equations. It outlines the steps involved, including solving one equation for a variable, substituting it into another equation, and solving for the remaining variable. Several examples are provided, demonstrating scenarios with unique solutions, no solutions, and infinite solutions. The tutorial concludes with a real-life application involving the purchase of turkey and veggie burgers.

What is the first step in solving systems of equations using substitution?

• Graph both equations to find the intersection point.

• Combine like terms in both equations.

• Solve one of the equations for one variable.

• Substitute one equation into the other and solve.

After substituting and solving for one variable, what is the next step?

• Graph the solution to verify.

• Solve the second equation for the other variable.

• There are no further steps.

• Substitute the found value back into the original equation.

In the example with equations y = 4x - 1 and y = 2x - 5, what is the value of x?

• 1

• -1

• 2

• -2

What does the solution (x, y) = (-2, -9) represent in the context of solving systems of equations?

• The point where both equations intersect on a graph.

• The coefficients of the linear equations.

• The slope of the equations.

• The y-intercept of the equations.

What is the significance of finding a solution like x = -1, y = -6 for a system of equations?

• It means the equations have no solution.

• It represents the unique point of intersection between the two lines.

• It indicates the equations are parallel.

• It shows the equations are identical.

What does it mean if, after substitution, you get a statement that is not true, like 12 = -1?

• The system has one solution.

• The equations are identical.

• The system has no solution.

• The system has infinitely many solutions.

If after substitution and simplification, the equation simplifies to a true statement like 54 = 54, what does it imply?

• The system has no solution.

• The system has exactly one solution.

• The system has infinitely many solutions.

• The equations are not related.

When solving a real-life problem involving a budget constraint, what is the first step?

• Determine the total cost.

• Set up equations based on quantities and costs.

• Calculate the total number of items.

• Graph the equations to find a solution.

In the real-life example, if you buy 50 items for $90, with two types of items priced differently, what kind of system do you set up?

• A single linear equation.

• A system of linear equations.

• A system of linear inequalities.

• A quadratic equation system.

How many turkey burgers were bought if 50 burgers were bought in total for $90, with turkey burgers costing $2 each and veggie burgers $1.50 each?

• 70

• 30

• 50

• 20