To find the solution of the system of equations given by \( y = 4x - 10 \) and \( y = -2x + 8 \), we need to find the point where the two lines intersect. This involves setting the equations equal to each other because, at the point of intersection, the \( y \)-values will be the same for both equations:
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Set the equations equal to each other: \[ 4x - 10 = -2x + 8 \]
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Solve for \( x \):
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First, add \( 2x \) to both sides: \[ 4x + 2x - 10 = 8 \] \[ 6x - 10 = 8 \]
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Next, add 10 to both sides: \[ 6x = 18 \]
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Now divide by 6: \[ x = 3 \]
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Now substitute \( x = 3 \) back into one of the original equations to find \( y \). We'll use the equation \( y = 4x - 10 \): \[ y = 4(3) - 10 \] \[ y = 12 - 10 \] \[ y = 2 \]
Therefore, the solution of the system of equations is: \[ (3, 2) \]
So the final answer is: The solution of the system of equations is \( (3, 2) \).
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