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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.

Buy a graphing calculator

Q: Two cars leave at the same time. One car drives North at a rate of 65 m/hr and the other car drives south at a rate of 55 m/hr. In how many hours will the cars be . . . → Read More: Rate problem, two cars leave at the same time

Coffee mixture word problem

Q: A coffee merchant has two types of coffee beans, one selling for $3 per pound and the other for $5 per pound. The beans are to be mixed to provide 100 pounds of a mixture selling for $4.18 per pound. How much of each type of coffee bean should be used to form . . . → Read More: Coffee mixture word problem

Perimeter of Triangle Word Problem

Q: The longest side of a triangle is four inches longer than the shortest side. The remaining side is two inches longer than the shortest side. The perimeter of the triangle ( the sum of the lengths of the sides) is 24 inches. what is the length of the longest side?

A: Let x . . . → Read More: Perimeter of Triangle Word Problem