To solve the system of equations using substitution, we start with the two equations:
- \( Y = 5x \)
- \( Y = 9x + 4 \)
Since both equations are equal to \( Y \), we can set them equal to each other:
\[ 5x = 9x + 4 \]
Now, we can solve for \( x \):
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Subtract \( 9x \) from both sides: \[ 5x - 9x = 4 \] \[ -4x = 4 \]
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Divide by -4: \[ x = -1 \]
Now that we have the value of \( x \), we can substitute it back into one of the original equations to find \( Y \). We can use the first equation \( Y = 5x \):
\[ Y = 5(-1) = -5 \]
Thus, the solution to the system of equations is:
\[ (x, Y) = (-1, -5) \]
So, the solution is \( x = -1 \) and \( Y = -5 \).
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