# How do you solve the following system: # 3x – 5y = 53 ,5x - 7y = 12 #?

##### 2 Answers

Why on earth do they chose such awful numbers????

#### Explanation:

In solving equations for variable values the method is to manipulate so that you have a load of values and just one variable. It is then solvable. Variables in this case being

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Consider equation(1)

To make the -5y positive multiply everything by -1

Add

But

Divide both sides by 5 ( this is the same as

But

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Using

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Substitute for

It does not matter which of the 2 equations you use.

#### Explanation:

There are several methods for solving a system of equations, also known as simultaneous equations. The method you choose will depend on the format of the equations you are given.

- Elimination - [make additive inverses and add the equations]
- Substitution - [write one variable in terms of the other]
- Equating - [one variable is expressed in two different ways]
- Matrices - [ multiply a matrix by its inverse to get the unit matrix]
- Graphically - [ graph each equation and find the intersection]

In this example I will use the elimination method.

Now that you have value for

.

[Note that:

This was done by multiplying B by