To solve the system of equations using the substitution method, we will first solve one of the equations for one variable and then substitute that expression into the other equation.
We have the following equations:
- \( Y = -4X \)
- \( Y = X - 5 \)
Since both equations are set equal to \( Y \), we can set them equal to each other:
\[ -4X = X - 5 \]
Next, we will solve for \( X \):
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Add \( 4X \) to both sides: \[ 0 = 5X - 5 \]
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Add \( 5 \) to both sides: \[ 5 = 5X \]
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Divide both sides by \( 5 \): \[ X = 1 \]
Now that we have the value of \( X \), we can substitute it back into one of the original equations to find \( Y \). We'll use the first equation:
\[ Y = -4X \]
Substituting \( X = 1 \):
\[ Y = -4(1) = -4 \]
The solution to the system of equations is:
\[ X = 1, \quad Y = -4 \]
Thus, the solution in ordered pair form is:
\[ (1, -4) \]
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