To solve the system of equations using substitution, we have the following equations:
- \( y = 3x - 4 \)
- \( y = -2x + 1 \)
Since both equations are equal to \( y \), we can set them equal to each other:
\[ 3x - 4 = -2x + 1 \]
Now, we will solve for \( x \).
- Add \( 2x \) to both sides:
\[ 3x + 2x - 4 = 1 \]
This simplifies to:
\[ 5x - 4 = 1 \]
- Next, add \( 4 \) to both sides:
\[ 5x = 5 \]
- Now, divide by \( 5 \):
\[ x = 1 \]
Now that we have \( x \), we can substitute \( x = 1 \) back into either of the original equations to find \( y \). We'll use the first equation:
\[ y = 3(1) - 4 \]
This simplifies to:
\[ y = 3 - 4 = -1 \]
So the solution to the system of equations is:
\[ (x, y) = (1, -1) \]
Final Answer: (1, -1)
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