Solving Systems of Equations with Substitution

The video tutorial covers solving systems of equations using substitution. It begins with an introduction and warm-up exercises, followed by detailed steps to solve equations by substitution. The instructor provides examples, discusses infinite and no solutions, and concludes with a final example. The video encourages students to pause and try solving problems independently.

What is the first step in solving for y in the equation 2x + y = 7?

• Divide both sides by 2

• Add 2x to both sides

• Multiply both sides by 2

• Subtract 2x from both sides

In the equation x - 4y = 7, what operation is needed to isolate x?

• Divide both sides by 4

• Multiply both sides by 4

• Add 4y to both sides

• Subtract 4y from both sides

When substituting y = 3x + 8 into another equation, what is the next step?

• Combine like terms

• Distribute the 3

• Add 3x to both sides

• Subtract 3x from both sides

After finding x = -5, where is the best place to substitute this value to find y?

• In the equation where x is isolated

• In any equation

• In the equation where y is already isolated

• In the original equation

What is the result of substituting x = -2 into y = 1 - 4x?

• y = -1 - 8

• y = -1 + 8

• y = 1 - 8

• y = 1 + 8

What does it mean if you get an equation like -42 = -42 after solving?

• There is a unique solution

• There are infinite solutions

• There is no solution

• The solution is x = 0

What should you do if you encounter a negative sign in front of y in an equation?

• Ignore it

• Add it to both sides

• Multiply or divide both sides by -1

• Subtract it from both sides

When solving for x in the equation x = -18 - 2y, what is the next step after isolating x?

• Substitute x into the other equation

• Distribute the -2

• Add 2y to both sides

• Combine like terms

What is the final step in solving a system of equations by substitution?

• Check the solution

• Write the solution as (x, y)

• Combine like terms

• Isolate y

What did the acorn want to study when it grew up?

• Biology

• Mathematics

• Physics

• Chemistry