Solving Linear Equations for y

The video tutorial explains how to solve the equation 10x + 5y = 80 for y. It begins by identifying the need to isolate y and applying inverse operations. The instructor highlights the importance of understanding the equation's components, such as the multiplication of y by 5 and the addition of 10x. The tutorial demonstrates rewriting the equation in standard form and simplifying it by dividing both sides by 5. The final solution is presented as y = -2x + 16, with a focus on ensuring clarity in each step of the process.

What is the initial equation given in the problem?

• 10x + 5y = 80

• 5x + 10y = 80

• 5x - 10y = 80

• 10x - 5y = 80

What is the first step to isolate the variable y?

• Divide both sides by 5

• Multiply both sides by 5

• Subtract 10x from both sides

• Add 10x to both sides

What does the addition sign in the equation indicate about 5y?

• 5y is negative

• 5y is positive

• 5y is zero

• 5y is a fraction

Why can't 80 and -10x be combined?

• They are already combined

• They are both constants

• They are both variables

• One has an x and the other does not

How should the equation be rewritten to follow standard form?

• 5y = 80 - 10x

• 5y = -80 + 10x

• 5y = -10x + 80

• 5y = 10x - 80

What is the next step after rewriting the equation in standard form?

• Divide both sides by 5

• Add 5 to both sides

• Multiply both sides by 5

• Subtract 5 from both sides

What is the result of dividing -10x by 5?

• 2x

• -2x

• -5x

• 5x

What is the result of dividing 80 by 5?

• 20

• 40

• 16

• 8

What is the final form of the equation for y?

• y = -2x + 16

• y = 2x - 16

• y = -2x - 16

• y = 2x + 16

Why is it important to understand that 5 divides into both terms?

• To subtract the terms correctly

• To add the terms correctly

• To simplify the equation correctly

• To multiply the terms correctly