Solve the system of equations: -x + y = -6 and -8x - 9y = 3, and provide the coordinates (x, y).
Understand the Problem
The question is asking to solve the system of equations provided and find the values of x and y. The high level approach involves using substitution or elimination methods to find the solution.
Answer
The solution is \((3, -3)\).
Answer for screen readers
The solution to the system of equations is ((3, -3)).
Steps to Solve
- Rearrangement of the First Equation
Start with the first equation: $$ -x + y = -6 $$ Rearranging gives: $$ y = x - 6 $$
- Substitution into the Second Equation
Now substitute (y) into the second equation: $$ -8x - 9(x - 6) = 3 $$
- Simplifying the Second Equation
Distributing ( -9 ) in the equation: $$ -8x - 9x + 54 = 3 $$ Combine like terms: $$ -17x + 54 = 3 $$
- Solving for x
Isolate (x): $$ -17x = 3 - 54 $$ $$ -17x = -51 $$ Dividing by (-17): $$ x = 3 $$
- Finding y value
Now substitute (x) back into the equation for (y): $$ y = 3 - 6 $$ So, $$ y = -3 $$
The solution to the system of equations is ((3, -3)).
More Information
The values (x = 3) and (y = -3) satisfy both equations in the system. Systems of linear equations can be solved using various methods, including substitution and elimination. It's useful to be familiar with both.
Tips
- Not correctly substituting (y) back into the second equation.
- Combining like terms incorrectly after substitution.
- Forgetting to isolate variables when solving equations.
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