SOLVING LINEAR EQUATIONSAlgebra 1 Mr. Saucedo

Objective

Learn how to identify linear equations. Learn tricks to solve linear equations.

True facts about linear equations The variables will always have 1 as exponent. Linear equation = linear function Two variables will never be multiplied. The graph of a linear equation is always a

line. Y = mx + b is called the equation of a line in

slope-intercept form. The y can be replaced with f(x).

Example: y = 3x + 2 is the same as: f(x) = 3x + 2.

Examples.

Linear equations Non linear equations

2x + 5 = -8 7a + b2 = 3X = 9 y = 1/xY = .5x x + xy = 16s – 3t = 8

5 xy

State whether each function is a linear function. Explain.

a) f(x) = 10 – 5x Yes!

It can be written as f(x) = – 5x + 10m = – 5, b = 10

b) g(x) = x4 – 5 No!

x has an exponent other than 1.

c) h(x, y) = 2xy No!

Two variables are multiplied together.

Linear Equations Linear Equations

Is it a linear equation?

NOTES: SOLVING THE LINEAR EQUATIONSSolving linear equations means finding the value of the variable that makes the equation true.

SOLVING LINEAR EQUATIONS:ONE STEP EQUATIONS

THERE IS ONE THING TO REMEMBER:

WHAT YOU DO TO ONE SIDE OF THE =

YOU DO TO THE OTHER!!!

GUIDED PRACTICE

Solve:

3)128(4

3x 54)5(3 xx

Guided Practice

Solve

34)36(3

2 xx 161.0)84.0(27. nn

CHECKPOINT

Solve )3(4)13(2 xx

Checkpoint

Solve xx 7)2(2

Independent practice

Solve the following equations.1. -5(4v – 3) = 1752. 205 = -8(4x – 1) + 53. -7(7 + x6x) + 4x = -2014. 3 – 5n = 3(1 – 6n)5. -7k + 27 = 3(1 – 6k) + 8k

Answers: 1. -8, 2. -6, 3. 4, 4. 0, 5. -8, 6. -14