Answer:
the solution to the system of equations is \( x = 3 \) and \( y = 7 \).
Step-by-step explanation:
To solve this system of equations by substitution, we'll first solve one equation for one variable and then substitute that expression into the other equation.
Given the equations:
1. \( y = 2x + 1 \)
2. \( -4x + 3y = 9 \)
We'll start by solving equation 1 for \( y \):
\[ y = 2x + 1 \]
Next, we'll substitute this expression for \( y \) into equation 2:
\[ -4x + 3(2x + 1) = 9 \]
Now, let's solve for \( x \):
\[ -4x + 6x + 3 = 9 \]
\[ 2x + 3 = 9 \]
\[ 2x = 6 \]
\[ x = 3 \]
Now that we have found \( x \), we can substitute it back into equation 1 to find \( y \):
\[ y = 2(3) + 1 \]
\[ y = 7 \]
So, the solution to the system of equations is \( x = 3 \) and \( y = 7 \).
