Identify Equations: Identify the system of equations to solve.We have two equations:1) 6x+2y=−262) x−6y=21We need to find the values of x and y that satisfy both equations simultaneously.
Choose Solution Method: Choose a method to solve the system of equations.We can use either substitution or elimination. For this problem, we will use the elimination method because it allows us to eliminate one variable by adding or subtracting the equations.
Multiply Second Equation: Multiply the second equation by 2 to make the coefficients of y in both equations equal in magnitude but opposite in sign.2×(x−6y)=2×21This gives us a new equation:2x−12y=42
Add Equations to Eliminate y: Add the new equation from Step 3 to the first equation to eliminate y.(6x+2y)+(2x−12y)=−26+42This simplifies to:8x−10y+2y−12y=168x−10y=16
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