2. 6 Solving Literal Equations for a Variable

California Standards Extension of 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

A formula is a type of literal equation A formula is a type of literal equation. A literal equation is an equation with two or more variables. To solve for one of the variables, use inverse operations.

Solving for a Variable Step 1 Locate the variable you are asked to solve for in the equation. Step 2 Identify the operations on this variable and the order in which they are applied. Step 3 Use inverse operations to undo operations and isolate the variable.

1) Solve 2x - 4y = 7 for x 2x - 4y = 7 + 4y + 4y 2x = 7 + 4y 2 2 2 2 Add 4y to both sides Simplify Divide both sides by 2 Does it simplify? This fraction cannot be simplified because both terms in the numerator are not divisible by 2.

2) Solve 2x - 4y = 7 for y To get y by itself, what is the first step? Add 2x Subtract 2x Add 4y Subtract 4y Answer Now

2x - 4y = 7 -2x - 2x -4y = 7 - 2x -4 -4 3) Solve 2x - 4y = 7 for y -4 -4 Subtract 2x from both sides Simplify Divide both sides by -4 Does it simplify? Nope!

4) Solve for y: 4x – 2y = 12 Subtract 4x from both sides Simplify - 4x - 4x -2y = 12 – 4x -2 -2 y = -6 + 2x or y = 2x - 6 Subtract 4x from both sides Simplify Divide both sides by -2 Does it simplify? Yes!

-4x + 12 4x - 12 -2x + 6 2x - 6 5) Solve for y: 4x – 2y = 12 Answer Now

9x – 7y = -7 1. Solve for x 2. Solve for y

Lesson Quiz: Part I Solve for the indicated variable. 1. 2. 3. 2x + 7y = 14 for y 4. for h P = R – C for C C = R – P for m m = x(k – 6) 5. for C C = Rt + S

Lesson Quiz: Part II Euler’s formula, V – E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. 6. Solve Euler’s formula for F. F = 2 – V + E 7. How many faces does a polyhedron with 8 vertices and 12 edges have? 6