Solve the system of equations: y = -2x - 9 and y = x - 3.
Understand the Problem
The question is asking to solve a system of two linear equations. This involves finding the values of x and y that satisfy both equations simultaneously.
Answer
The solution is $(-2, -5)$.
Answer for screen readers
The solution to the system of equations is $(-2, -5)$.
Steps to Solve
-
Identify the equations The two equations given are: $$ y = -2x - 9 $$ $$ y = x - 3 $$
-
Set the equations equal to each other Since both equations equal $y$, we can set them equal to each other: $$ -2x - 9 = x - 3 $$
-
Solve for $x$ Move $x$ to the left side and add 9 to both sides: $$ -2x - x = -3 + 9 $$ This simplifies to: $$ -3x = 6 $$ Now divide by -3: $$ x = -2 $$
-
Substitute $x$ back into one equation Use the value of $x$ in one of the original equations to find $y$: $$ y = -2(-2) - 9 $$ Calculating this gives: $$ y = 4 - 9 $$ So: $$ y = -5 $$
-
Write the solution as an ordered pair The solution to the system of equations is: $$ (x, y) = (-2, -5) $$
The solution to the system of equations is $(-2, -5)$.
More Information
The system of linear equations represents two lines on a graph. The point $(-2, -5)$ is where these two lines intersect. This means that at this point, both equations are satisfied.
Tips
- Mixing up signs: Be careful when moving terms across the equation; make sure to change the signs accordingly.
- Not substituting correctly: Ensure you substitute the value of $x$ into one of the original equations accurately.
AI-generated content may contain errors. Please verify critical information
