# Solve -2[[x,-1],[3,5]]+[[3,8],[-1,6]]=[[x,10],[-7,-4]] Multiply by each element of the matrix.
Simplify each element of the matrix .
Rearrange .
Rearrange .
Rearrange .
Find the function rule.
Check if the function rule is linear.
To find if the table follows a function rule, check to see if the values follow the linear form .
Build a set of equations from the table such that .
Calculate the values of and .
Simplify each equation.
Simplify each term.
Move to the left of .
Simplify each term.
Subtract from .
Move to the left of .
Simplify each term.
Move to the left of .
Solve for in the first equation.
Rewrite the equation as .
Subtract from both sides of the equation.
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify each equation.
Simplify .
Remove parentheses.
Subtract from .
Simplify .
Remove parentheses.
Subtract from .
Solve for in the second equation.
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify.
Simplify .
Multiply by .
Subtract from .
Simplify .
Multiply by .
Since , the equation will always be true.
Always true
Remove any equations from the system that are always true.
List the solutions to the system of equations.
Always true
List all of the solutions.
Calculate the value of using each value in the relation and compare this value to the given value in the relation.
Calculate the value of when , , and .
Simplify each term.
Multiply by .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Calculate the value of when , , and .
Simplify each term.
Multiply by .
Subtract from .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Calculate the value of when , , and .
Simplify each term.
Multiply by .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Since for the corresponding values, the function is linear.
The function is linear
The function is linear
The function is linear
Since all , the function is linear and follows the form .
Find .
Use the function rule equation to find .
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
Combine the opposite terms in .