To solve the system of equations using substitution, we'll follow these steps:
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We have the two equations: \[ Y = 3x - 50 \quad \text{(1)} \] \[ Y = -2x \quad \text{(2)} \]
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Since both equations equal \(Y\), we can set them equal to each other: \[ 3x - 50 = -2x \]
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Now, let's solve for \(x\):
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First, add \(2x\) to both sides: \[ 3x + 2x - 50 = 0 \] \[ 5x - 50 = 0 \]
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Next, add 50 to both sides: \[ 5x = 50 \]
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Finally, divide by 5: \[ x = 10 \]
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Now that we have \(x\), we can substitute this value back into either of the original equations to find \(Y\). We'll use equation (2): \[ Y = -2x \] Substituting \(x = 10\): \[ Y = -2(10) = -20 \]
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So, the solution to the system of equations is: \[ (x, Y) = (10, -20) \]
Thus, the result is \(x = 10\) and \(Y = -20\).
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