Solving Systems of Equations by Substitution

The video tutorial explains how to solve systems of linear equations using the substitution method. It begins with an introduction to the concept, followed by multiple examples demonstrating the step-by-step process of isolating variables and substituting them into equations to find solutions. The tutorial covers various scenarios, including cases where variables are already isolated and those requiring manipulation. The video concludes with a summary of the key points and techniques for effectively using substitution.

What is the first step in solving a system of linear equations using substitution?

• Add both equations together.

• Multiply both equations by the least common multiple.

• Graph both equations on a coordinate plane.

• Isolate one of the variables in either equation.

What is the solution to the system of equations where y = 2x + 1 and y = -3x + 11?

• (2, 5)

• (3, 7)

• (1, 3)

• (-1, -2)

After substituting the expression from one equation into the other, what should you do next?

• Check the solution in both original equations.

• Graph the resulting equation.

• Substitute the expression back into the original equation.

• Solve for the remaining variable.

How do you find the y-value after solving for x using substitution?

• Multiply the x-value by the coefficient of y.

• Substitute the x-value into the substituted equation.

• Substitute the x-value into the original equation.

• Add the x-value to the constant term.

In the third example, what is the first step to isolate a variable?

• Divide both sides by 2.

• Subtract 2y from both sides.

• Multiply both sides by 2.

• Add 2y to both sides.

What is the result when you substitute y = 5x - 2 into -3x + 6y = -12?

• -3x + 30x - 12 = -12

• -3x + 6(5x - 2) = -12

• 3x + 6(5x + 2) = 12

• -3x - 6(5x - 2) = 12

What is the coordinate point solution for the system of equations in example 4?

• (2, 5)

• (0, -2)

• (-4, 6)

• (3, 1)

For the fifth example, after isolating y, what is the correct substitution into the second equation?

• y = x - 4 into 4x - 6(x - 4) = 16

• y = x - 4 into -4x + 6(x - 4) = 16

• y = x + 4 into -4x - 6(x + 4) = -16

• y = x - 4 into -4x - 6(x - 4) = -16

What is the final step to find the solution for a system of equations using substitution?

• Multiply the equations by their coefficients.

• Divide the equations by the coefficient of the isolated variable.

• Graph the solution on a coordinate plane.

• Substitute the found value back into one of the original equations.

What is the solution for the system of equations in the last example?

• (-4, 6)

• (4, 0)

• (3, 6)

• (2, 5)