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The system of equations are , and .
Solve the system of equations by elimination method.
Step 1:
Eliminate one variable by using two pairs of equations.
Subtract the 2nd and 3rd equations to eliminate the one variable.
Step 2:
Solve the system of two equations containing and to find value.
(Divide each side by )
(Cancel common terms)
Substitute into any one of the original equation to find value.
(Third equation)
(Substitute )
(Multiply)
(Subtract from each side)
(Apply additive inverse property: )
(Divide each side by )
(Cancel common terms)
Step 3:
Substitute values of and into one of the original equation to find value.
(Second equation)
(Substitute and )
(Multiply)
(Combine like terms)
(Add to each side)
(Apply additive inverse property: )
(Divide each side by )
(Cancel common terms)
Thereore, the solution is , and .
Check solutions for and values.
(Second equation)
(Substitute , and )
(Multiply)
(Add: )
The solution of the system is .
The solution of the system is .
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