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### Like us? ## Intro to Systems of Equations

Systems of Equations deals with more than one equation. At first, you will usually be seeing two equations. If you are asked to solve the system, you are being asked to find the point(s) of intersection between the two graphs.

For example, let’s look at two lines:

Equation 1: Equation 2:

Recall the . . . → Read More: Intro to Systems of Equations

## Solving Systems of Equations with the Elimination Method (Addition)

Systems of Equations, where you have more than one equation and are trying to find the intersection between them, can be solved in a number of ways. Here we will look at the Elimination Method, also known as the Addition/Subtraction method.

Let’s look at a simple system of equations:

Equation 1: 3x+7y=11 Equation 2: . . . → Read More: Solving Systems of Equations with the Elimination Method (Addition)

## Solving Systems of Equations with the Elimination Method (Subtraction)

Systems of Equations, where you have more than one equation and are trying to find the intersection between them, can be solved in a number of ways. Here we will look at the Elimination Method, also known as the Addition/Subtraction method.

Let’s look at a simple system of equations:

Equation 1: 3x+5y=12 Equation 2: . . . → Read More: Solving Systems of Equations with the Elimination Method (Subtraction)

## Solving Systems of Equations by Substitution

Hopefully you have already learned how to solve systems of equations by graphing. If not, view our guide here.

Now we’re going to learn how to solve them by using algebra and a method called substitution.

Again, let’s look at the same two equations:

Equation 1: Equation 2:

Notice that both of the . . . → Read More: Solving Systems of Equations by Substitution

## Perimeter of a Rectangle, Two Unknowns

Q: The perimeter of a rectangle is 74 inches. If the width is doubled and the length is halved, the new rectangle will have a perimeter is 76 inches. What are the dimensions?

A: You have two unknowns, l=length and w=width, so you need two equations.

Recall that perimeter of a rectangle is P . . . → Read More: Perimeter of a Rectangle, Two Unknowns

## Investment Word Problem

Q: Hakim invested \$15000. He put part of it in a term deposit that paid 4% per annum, and the remainder in a treasury bill that paid 5% per annum. After one year, the total interest was \$690. How much did Hakim invest at each rate?

A: You have two unknowns (the amounts invested . . . → Read More: Investment Word Problem

## Trail mix, mixture word problem

Q: The manager of a bulk foods establishment sells a trail mix for \$10 per pound and premium cashews for \$15 per pound. The manager wishes to make a 100-pound trail mix-cashew mixture that will sell for \$14 per pound. How many pounds of each should be used?

A: Let x = pounds of . . . → Read More: Trail mix, mixture word problem

## Rate problem, two cars leave at the same time

Graph and then solve these equations by finding their point of intersection.