Lesson Solving Systems of Equations by Substitution

Source code of 'Solving Systems of Equations by Substitution'

This Lesson (Solving Systems of Equations by Substitution) was created by by Alwayscheerful(414)

: View Source, Show
About Alwayscheerful: I'm available as an online paid tutor if anyone need extensive 1 on 1 help. =)

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
{{{system( 2x+5y=-10, 3x-y=4 ) }}}

you can transform one equation so that a variable is by itself.  Solving equation 2 for y in terms of x gives you:
{{{-y=-3x+4}}}
Multiply the whole equation by -1 to get rid of the negative y
{{{y=3x-4}}}

Where the graphs intersect, the y in one equation stands for the same number as the y in the other.  So you may substitute {{{3x-4}}} for the y in Equation 1.

{{{2x+5(3x-4)=-10}}}

The result is an equation with only one variable.  Solve it for x.
Distribute the 5
{{{2x+15x-20=-10}}
Combine like terms; add 20 to each number
{{{17x=10}}}
Divide each side by 17
{{{x=10/17}}}
If you want decimal form, 
{{{x=.5882}}}
I would use fraction form because it is easier to use.

Substitute your answer for x into the other equation to get your y value.

{{{y=3(10/17)-4}}}
{{{y=(30/17)-4}}}
{{{y=-38/17}}}

Now you have your solution:
10/17 and -38/17

If you have attempted to solve by graphing, you would end up with this:
{{{graph(500,400,-10,10,-10,10,3x-4,(-2/5)x-2)}}}

CHECK YOUR ANSWER:
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.

{{{2(10/17)+5(-38/17)=-10}}}
*[invoke explain_simplification "2(10/17)+5(-38/17)=-10"]
Your answer is correct!
Hope this helps!