1.5 Equations with Multi-Variables

• We now know how to solve equations in terms of a single variable

• Like expressions, many equations could have more than 1 variable, especially formulas

Solving with Multiple Variables

• As always, you will have a designated variable to solve for

• All other variables are treated as constants– Operations will not change simply because there

are so many letters or what not– Still going to use inverse operations; allowed to

group variables together as one, if needed

• Sometimes, checking your answer may be difficult, so do your best to track your steps and see where you end up

• Example. The circumference of a circle is C = πd, where d is the diameter and C is the circumference. Write the new equation in terms of the diameter.

• Example. Solve the equation V = lwh, the volume of a rectangle, for h.

• Example. Solve the equation I = prt for r.

Values

• At times, you will be given the value of a variable, and be asked to solve for the year; in these cases, you should be able to check your answer easily

• Example. For the equation 2y + x = 5x + 6, find the value of y when x = -3 and x = 6

• Example. Find the value of y for the given value x = 2

• 58

7

4

3 yx

Applications

• Similar to expressions, we can write equations with multi-variables to model various things

• Especially helpful in regards to business and business modeling– Why?

• Example. You just opened a new store to sell Maclay merchandise and you want to determine how much cash money you will make. You start by selling shirts and hats; each shirt costs $12, while each hat will be $21. For each item you sell, you decide to give back $3 for a scholarship fund. Write an equation to model your profit.

• Example. Using the previous equation, determine the number of hats sold if you made $324 in one week and know you sold 10 shirts.

• Activity• Attempt to write your own word problem,

with a partner, using an equations with more than one variable.

• Assignment• Pg. 36• 13-17 odd, 22-32 even, 34-36, 38-40, 57