Bot GPT 4-o mini To solve the system of equations provided, we will first rewrite the equations clearly, as there seem to be some formatting issues in your message.
From your message, it looks like we have:
- \( 2y = 3x + 43 \)
- \( 4x - 2y = -44 \)
Let’s work through this step-by-step using the substitution method.
Step 1: Solve the first equation for \( y \)
From the first equation:
\[ 2y = 3x + 43 \]
Divide both sides by 2:
\[ y = \frac{3x + 43}{2} , \text{(Equation 1)} \]
Step 2: Substitute \( y \) into the second equation
Now we can substitute \( y \) from Equation 1 into the second equation \( 4x - 2y = -44 \):
\[ 4x - 2\left(\frac{3x + 43}{2}\right) = -44 \]
Step 3: Simplify the second equation
This simplifies to:
\[ 4x - (3x + 43) = -44 \]
Now, expand and combine like terms:
\[ 4x - 3x - 43 = -44 \]
This simplifies to:
\[ x - 43 = -44 \]
Step 4: Solve for \( x \)
Add 43 to both sides:
\[ x = -44 + 43 \]
So,
\[ x = -1 \]
Step 5: Substitute \( x \) back to find \( y \)
Now we substitute \( x = -1 \) back into Equation 1 to find \( y \):
\[ y = \frac{3(-1) + 43}{2} \]
Calculate the numerator:
\[ y = \frac{-3 + 43}{2} = \frac{40}{2} = 20 \]
Final Solution
Thus, the solution to the system of equations is:
\[ x = -1, \quad y = 20 \]
We can express the solution as an ordered pair:
\[ (x, y) = (-1, 20) \]
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