# Lesson Solving Systems of Equations by Substitution

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This Lesson (Solving Systems of Equations by Substitution) was created by by Alwayscheerful(414)  : View Source, Show
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Finding intersection points by actual graphing has two disadvantages. It is tedious and it is of limited accuracy. In this lesson, you will learn how to calculate such intersection points.
A pair of equations with the same two variables is called a system of equations. The ordered pair where the graphs intersect each other makes both equations true. It is called the solution of the system.

Example 1
To solve the system

you can transform one equation so that a variable is by itself. Solving equation 2 for y in terms of x gives you:

Multiply the whole equation by -1 to get rid of the negative y

Where the graphs intersect, the y in one equation stands for the same number as the y in the other. So you may substitute for the y in Equation 1.

The result is an equation with only one variable. Solve it for x.
Distribute the 5

Divide each side by 17

If you want decimal form,

I would use fraction form because it is easier to use.

10/17 and -38/17

If you have attempted to solve by graphing, you would end up with this:

To check, all you need to do is plug the values for x and y into one of the equations. If the statement is true, your answers are correct. If it is false, your answers are incorrect.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: Graphical form: Equation was fully solved.Text form: 2*(10/17)+5*(-38/17)=-10 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 2*(10/17)+5*(-38/17)=-10 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

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Remove unneeded parentheses around factor ,
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Remove unneeded parentheses around factor ,
It becomes .

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Multiplied numerator integers
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Multiplied numerator integers
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Factors 170 and 17 have greatest common factor (GCF) of 17. Reducing fraction.
It becomes .

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Remove extraneous '1' from product
It becomes .

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Moved these terms to the left
It becomes .

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