Solve the following system of equations using substitution: y = 6x + 9 y = x - 6
Understand the Problem
The question asks to solve a system of two linear equations using the substitution method. This involves solving for one variable in terms of the other and substituting that expression into the other equation.
Answer
$(-3, -9)$
Answer for screen readers
$(-3, -9)$
Steps to Solve
-
Set the equations equal to each other Since both equations are equal to $y$, we can set them equal to each other: $$6x + 9 = x - 6$$
-
Solve for $x$ Subtract $x$ from both sides: $$5x + 9 = -6$$ Subtract 9 from both sides: $$5x = -15$$ Divide by 5: $$x = -3$$
-
Substitute $x$ back into one of the equations to solve for $y$ We can use the second equation $y = x - 6$. Substitute $x = -3$ to get: $$y = -3 - 6$$ $$y = -9$$
-
Write the solution as a coordinate pair The solution is the point where the two lines intersect, which is $(-3, -9)$.
$(-3, -9)$
More Information
The solution to a system of linear equations represents the point where the lines intersect on a graph. If the lines are parallel, there is no solution. If they are the same line, there are infinitely many solutions.
Tips
A common mistake is making errors when isolating the variables, especially with negative signs. Another mistake is solving for $x$ but forgetting to substitute back to find $y$.
AI-generated content may contain errors. Please verify critical information
