To solve the system of equations by substitution, follow these steps:
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Set the equations: \[ Y = 6x + 10 \quad (1) \] \[ Y = 4x \quad (2) \]
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Substitute equation (2) into equation (1): Since both equations equal \(Y\), we can set them equal to each other: \[ 6x + 10 = 4x \]
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Solve for \(x\): Subtract \(4x\) from both sides: \[ 6x - 4x + 10 = 0 \] This simplifies to: \[ 2x + 10 = 0 \] Now, subtract 10 from both sides: \[ 2x = -10 \] Divide by 2: \[ x = -5 \]
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Substitute \(x\) back into either equation to find \(Y\): We can use equation (2): \[ Y = 4x = 4(-5) = -20 \] So, \(Y = -20\).
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Write the solution as an ordered pair: The solution to the system of equations is: \[ (x, Y) = (-5, -20) \]
Thus, the solution to the system of equations is \((-5, -20)\).