Linear and Quadratic Equations

Back to: MATHEMATICS SS3

Welcome to class! 

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

Linear and Quadratic Equations

Applications

• Linear equations:

1. Pricing Problems
2. Distance/Rate Problems
3. Work/Rate Problems
4. Mixing Problems

• Quadratic equations:

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.

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