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8. \( \left\{\begin{array}{l}y=3 x \\ y=x-2\end{array}\right. \)

Ask by Stephens Murray. in the United States
Mar 14,2025

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\( x=-1 \) and \( y=-3 \).

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To solve the system of equations, we start by substituting \(y = 3x\) into the second equation \(y = x - 2\): \[ 3x = x - 2 \] Now, let's solve for \(x\). By subtracting \(x\) from both sides, we get: \[ 3x - x = -2 \] This simplifies to: \[ 2x = -2 \] Dividing both sides by 2 gives: \[ x = -1 \] Next, we substitute \(x = -1\) back into the first equation to find \(y\): \[ y = 3(-1) = -3 \] Therefore, the solution to the system of equations is \( (x, y) = (-1, -3) \). Just double-checking, if we plug \(x = -1\) into the second equation: \[ y = -1 - 2 = -3 \] So, it’s consistent! The intersection point of the lines represented by the equations is \((-1, -3)\).

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