To solve the system of equations using substitution, we'll follow these steps:
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We have the two equations: \[ y = -4x - 6 \quad \text{(1)} \] \[ y = -3x - 3 \quad \text{(2)} \]
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Since both equations are equal to \(y\), we can set them equal to each other: \[ -4x - 6 = -3x - 3 \]
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Now, we will solve for \(x\):
- First, add \(4x\) to both sides: \[ -6 = x - 3 \]
- Next, add \(3\) to both sides: \[ -6 + 3 = x \] \[ -3 = x \]
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Now that we have \(x = -3\), we can substitute this value back into either original equation to find \(y\). We'll use equation (1): \[ y = -4(-3) - 6 \] \[ y = 12 - 6 \] \[ y = 6 \]
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The solution to the system of equations is: \[ (x, y) = (-3, 6) \]
Thus, the point of intersection and the solution to the system of equations is: \[ \boxed{(-3, 6)} \]
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