Linear Algebra Examples

Solve by Substitution 4=x+4y , y+x=2
,
Step 1
Subtract from both sides of the equation.
Step 2
Replace all occurrences of with in each equation.
Tap for more steps...
Step 2.1
Replace all occurrences of in with .
Step 2.2
Simplify the right side.
Tap for more steps...
Step 2.2.1
Simplify .
Tap for more steps...
Step 2.2.1.1
Simplify each term.
Tap for more steps...
Step 2.2.1.1.1
Apply the distributive property.
Step 2.2.1.1.2
Multiply by .
Step 2.2.1.1.3
Multiply by .
Step 2.2.1.2
Subtract from .
Step 3
Solve for in .
Tap for more steps...
Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from .
Step 3.3
Divide each term in by and simplify.
Tap for more steps...
Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
Tap for more steps...
Step 3.3.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
Tap for more steps...
Step 3.3.3.1
Dividing two negative values results in a positive value.
Step 4
Replace all occurrences of with in each equation.
Tap for more steps...
Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify the right side.
Tap for more steps...
Step 4.2.1
Simplify .
Tap for more steps...
Step 4.2.1.1
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.2
Combine and .
Step 4.2.1.3
Combine the numerators over the common denominator.
Step 4.2.1.4
Simplify the numerator.
Tap for more steps...
Step 4.2.1.4.1
Multiply by .
Step 4.2.1.4.2
Subtract from .
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