Determine the point of intersection for the system of equations: \( y = 3x - 4 \) and \( y = -2x + 8 \)
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To find the point of intersection, we need to set the two equations equal to each other since they both equal \(y\). Thus, we have: \[ 3x - 4 = -2x + 8 \] Now, let's solve for \(x\): 1. Add \(2x\) to both sides: \[ 3x + 2x - 4 = 8 \] \[ 5x - 4 = 8 \] 2. Next, add \(4\) to both sides: \[ 5x = 12 \] 3. Finally, divide by \(5\): \[ x = \frac{12}{5} = 2.4 \] Now that we have the \(x\) value, substitute \(x = 2.4\) back into either original equation to find \(y\). Using the first equation: \[ y = 3(2.4) - 4 \] \[ y = 7.2 - 4 \] \[ y = 3.2 \] Thus, the point of intersection is \(\left( \frac{12}{5}, \frac{16}{5} \right)\) or (2.4, 3.2). So, the point of intersection for the given system of equations is \((2.4, 3.2)\).