Lesson Solving Systems of Equations by Substitution

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

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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
system%28+2x%2B5y=-10%2C+3x-y=4+%29+

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%2B4

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%2B5%283x-4%29=-10

The result is an equation with only one variable. Solve it for x.
Distribute the 5
2x%2B15x-20=-10%7D%7D%0D%0ACombine+like+terms%3B+add+20+to+each+number%0D%0A%7B%7B%7B17x=10

2x%2B15x-20=-10%7D%7D%0D%0ACombine+like+terms%3B+add+20+to+each+number%0D%0A%7B%7B%7B17x=10

Divide each side by 17
x=10%2F17

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%2810%2F17%29-4

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%28500%2C400%2C-10%2C10%2C-10%2C10%2C3x-4%2C%28-2%2F5%29x-2%29

graph%28500%2C400%2C-10%2C10%2C-10%2C10%2C3x-4%2C%28-2%2F5%29x-2%29

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%2810%2F17%29%2B5%28-38%2F17%29=-10

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

YOUR ANSWER

Graphical form: Equation was fully solved.
Text form: 2*(10/17)+5*(-38/17)=-10 simplifies to 0=0
Cartoon (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.