Solve the system of equations: y = -8x + 10 and y = -2x - 2.

Understand the Problem

The question is asking for the solution(s) to the system of equations given by the two lines: y = -8x + 10 and y = -2x - 2. We need to find the point of intersection or the values of x and y where both equations are satisfied.

Answer

The solution is $ (2, -6) $.

Steps to Solve

Set the equations equal to each other

Since both equations are equal to ( y ), we can set them equal to find ( x ): $$ -8x + 10 = -2x - 2 $$

Isolate the variable ( x )

First, add ( 8x ) to both sides: $$ 10 = 6x - 2 $$

Next, add ( 2 ) to both sides: $$ 12 = 6x $$

Solve for ( x )

Now, divide both sides by ( 6 ): $$ x = 2 $$

Substitute ( x ) back into one of the original equations

We can use either equation; let's use the first one: $$ y = -8(2) + 10 $$

Calculate ( y )

Perform the multiplication and addition: $$ y = -16 + 10 $$ $$ y = -6 $$

The solution to the system of equations is ( (2, -6) ).

More Information

The point ( (2, -6) ) is where the two lines represented by the equations intersect. This means that at ( x = 2 ), both equations yield the same value for ( y ).

Tips

Not setting the equations equal: A common mistake is failing to set the equations equal when looking for the intersection point. Ensure both equations are expressed in the same form.
Arithmetic errors: Be careful with arithmetic when isolating or solving for variables; double-check calculations.

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