Chapter 2

This is the linear equation with one equation

ax+b=0

This is the linear equation with two variables

ax + by = c

• Find the LCD (12)

• Multiply both sides by the least common denominator.

• Simplify

Solve for x if y= 0.72

• y=1.312x-2.56

0.72=1.312x-2.56

Add 2.56 to both sides and then divide by 1.312 to find x.

x= 2.5

This is any number a for f(a)=0

A zero of a function.

What are zeros also called?

• X-intercepts

• Real zeros

• Real Solutions

This is a collection of linear equations containing the same set of variables

A system of equations.

Solving Break Even: R=5585x and T(C)=61,740+440x

• Y1= 5585x

• Y2= 61,740+440x

• Find point where they intersect

• Isolate the Y by subtracting x value on both sides

• Divide both equations by the Y coefficient

• Find where they intersect

How do we solve via substitution?

1) Solve one equation for a variable,

2) Substitute that variable into the other equation.

! Isolate the Y !

Find x value and substitute it into the equation with the isolated y

Plug the x value into an equation to get the y

Unique Solutions

No solutions

Infinite Solutions

This is a statement that one quantity or expression is greater than, less than, greater than or equal to, or less than or equal to another

What is an inequality

• Graph these lines, and find their point of intersection

These are inequalities that are connected by the words and or or. These can be solved algebraically or graphically

What are double inequalities?

A student has taken four tests and has earned grades of 90%, 83%, 93%, and 85%. IF all five tests count the same, what grade must the student earn on the final test so that the average is at least 80% and less than 90%?

80<90+88+93+85+x/5<9

• 80< 356+x/5<90

• 400<365 +x <450

• 44<x<94