 Welcome to class!

In today’s class, we will be talking about linear and quadratic equations. Enjoy the class! #### Applications

• ##### Linear equations:
1. Pricing Problems
2. Distance/Rate Problems
3. Work/Rate Problems
4. Mixing Problems
1. Projectile motion problems
2. Geometry area problems
3. Distance/Rate Problems
##### One Linear – One Quadratic

A linear equation does not contain any powers higher than 1.

A quadratic equation is an equation with the highest power of 2.

For example:

y = x + 3 is a linear equation and y = x2 + 3x is a quadratic equation.

##### Solving simultaneous equations with one linear and one quadratic

When solving simultaneous equations with a linear and quadratic equation, there will usually be two pairs of answers.

y = x + 3

y = x2 + 3x

Substitute y = x + 3 into the quadratic equation to create an equation which can be factorised and solved.

x + 3 = x2 + 3x

Rearrange the equation to get all terms on one side, so subtract x and -3 from both sides:

x + 3 – x – 3 = x2 + 3x – x – 3

0 = x2 + 2x – 3

Factorise this equation:

(x + 3) (x – 1) = 0

If the product of two brackets is zero, then one or both brackets must also be equal to zero.

To solve, put each bracket equal to zero.

x + 3 = 0

x = -3

x – 1 = 0

x = 1

To find the values for y, substitute the two values for x into the original linear equation.

y = x + 3 when x = -3

y = -3 + 3

y = 0

y = x + 3 when x = 1

y = 1 + 3

y = 4

The answers are now in pairs: when x = -3, y = 0 and when x = 1, y = 4.

In our next class, we will be talking about Surface areas and volume of spheres and hemispheres. We hope you enjoyed the class.

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.