Solve the system of equations: y = -3x - 8 and y = -2x - 2.

Understand the Problem

The question is asking us to solve a system of equations given in slope-intercept form. We need to find the values of x and y that satisfy both equations simultaneously.

Answer

$(-6, 10)$

Steps to Solve

Set the equations equal to each other
To find the intersection of the two lines (where they both equal the same $y$ value), set the equations equal:
$$ -3x - 8 = -2x - 2 $$
Isolate the variable $x$
Rearranging the equation to get all $x$ terms on one side and constant terms on the other:
$$ -3x + 2x = -2 + 8 $$ This simplifies to:
$$ -x = 6 $$
Solve for $x$
Now, divide both sides by -1 to find $x$:
$$ x = -6 $$
Substitute $x$ back to find $y$
Choose either original equation to substitute $x = -6$. We'll use the first equation:
$$ y = -3(-6) - 8 $$ Calculating gives:
$$ y = 18 - 8 = 10 $$
Write the solution
The solution to the system of equations is:
$$ (x, y) = (-6, 10) $$

The solution to the system of equations is $(-6, 10)$.

More Information

This solution represents the point where the two lines intersect on a graph. Systems of equations can be solved graphically, algebraically, or using substitution or elimination methods.

Tips

Not isolating $x$ correctly when manipulating the equation.
Forgetting to substitute back into one of the original equations, leading to an incomplete solution.
Miscalculating when performing arithmetic operations.

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