Linear Algebra Examples

Solve by Substitution 4x+3y+7=0 , 5x-2y+3=0
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Step 1
Solve for in .
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Step 1.1
Move all terms not containing to the right side of the equation.
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Step 1.1.1
Subtract from both sides of the equation.
Step 1.1.2
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
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Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
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Step 1.2.2.1
Cancel the common factor of .
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Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
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Step 1.2.3.1
Simplify each term.
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Step 1.2.3.1.1
Move the negative in front of the fraction.
Step 1.2.3.1.2
Move the negative in front of the fraction.
Step 2
Replace all occurrences of with in each equation.
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Step 2.1
Replace all occurrences of in with .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Simplify each term.
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Step 2.2.1.1.1
Apply the distributive property.
Step 2.2.1.1.2
Multiply .
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Step 2.2.1.1.2.1
Multiply by .
Step 2.2.1.1.2.2
Combine and .
Step 2.2.1.1.2.3
Multiply by .
Step 2.2.1.1.3
Multiply .
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Step 2.2.1.1.3.1
Multiply by .
Step 2.2.1.1.3.2
Combine and .
Step 2.2.1.1.3.3
Multiply by .
Step 2.2.1.1.4
Simplify each term.
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Step 2.2.1.1.4.1
Move the negative in front of the fraction.
Step 2.2.1.1.4.2
Move the negative in front of the fraction.
Step 2.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.3
Combine and .
Step 2.2.1.4
Combine the numerators over the common denominator.
Step 2.2.1.5
Combine the numerators over the common denominator.
Step 2.2.1.6
Multiply by .
Step 2.2.1.7
Subtract from .
Step 2.2.1.8
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.9
Simplify terms.
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Step 2.2.1.9.1
Combine and .
Step 2.2.1.9.2
Combine the numerators over the common denominator.
Step 2.2.1.10
Simplify the numerator.
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Step 2.2.1.10.1
Multiply by .
Step 2.2.1.10.2
Subtract from .
Step 2.2.1.10.3
Factor out of .
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Step 2.2.1.10.3.1
Factor out of .
Step 2.2.1.10.3.2
Factor out of .
Step 2.2.1.10.3.3
Factor out of .
Step 2.2.1.11
Simplify with factoring out.
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Step 2.2.1.11.1
Factor out of .
Step 2.2.1.11.2
Rewrite as .
Step 2.2.1.11.3
Factor out of .
Step 2.2.1.11.4
Simplify the expression.
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Step 2.2.1.11.4.1
Rewrite as .
Step 2.2.1.11.4.2
Move the negative in front of the fraction.
Step 3
Solve for in .
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Step 3.1
Set the numerator equal to zero.
Step 3.2
Solve the equation for .
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Step 3.2.1
Divide each term in by and simplify.
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Step 3.2.1.1
Divide each term in by .
Step 3.2.1.2
Simplify the left side.
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Step 3.2.1.2.1
Cancel the common factor of .
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Step 3.2.1.2.1.1
Cancel the common factor.
Step 3.2.1.2.1.2
Divide by .
Step 3.2.1.3
Simplify the right side.
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Step 3.2.1.3.1
Divide by .
Step 3.2.2
Subtract from both sides of the equation.
Step 4
Replace all occurrences of with in each equation.
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Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify the right side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Combine the numerators over the common denominator.
Step 4.2.1.2
Simplify the expression.
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Step 4.2.1.2.1
Multiply by .
Step 4.2.1.2.2
Subtract from .
Step 4.2.1.2.3
Divide by .
Step 5
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 6
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 7