\( \begin{array}{l}y=-2 x \\ y=8 x-10\end{array} \) Answer Attempt 1 out of 2 \( (\square, \square) \) Submit Answer

To find the intersection of the lines given by the equations \( y = -2x \) and \( y = 8x - 10 \), you can set the right-hand sides equal to each other: \[ -2x = 8x - 10 \] By solving for \( x \), you add \( 2x \) to both sides: \[ 0 = 10x - 10 \] Next, add 10 to both sides: \[ 10 = 10x \] Now, divide both sides by 10: \[ x = 1 \] Now that you have \( x \), plug it back into either original equation to find \( y \). Using \( y = -2x \): \[ y = -2(1) = -2 \] So the intersection point is \( (1, -2) \). Now, if we think about real-world applications, the intersection of lines can represent a point where two different scenarios converge. For example, in economics, it could indicate the equilibrium price where supply and demand meet, leading to insights in market strategies! Also, when solving systems of equations like this, a common mistake is to forget to check if the lines are parallel or coincident. Remember, if the slopes are the same (for instance, if both lines had the form \( y = mx + b \) with the same \( m \)), they would never intersect! Keep a keen eye on those coefficients!