To find the solution to the system of linear equations given by:
- \( 3x - 2y = -4 \)
- \( x - 5y = 3 \)
we can solve the equations using substitution or elimination. In this case, let's use substitution.
First, solve the second equation for \( x \):
\[ x = 5y + 3 \]
Now, substitute this expression for \( x \) into the first equation:
\[ 3(5y + 3) - 2y = -4 \]
Expand and simplify:
\[ 15y + 9 - 2y = -4 \]
Combine like terms:
\[ 13y + 9 = -4 \]
Subtract 9 from both sides:
\[ 13y = -4 - 9 \] \[ 13y = -13 \]
Now, divide by 13:
\[ y = -1 \]
Next, substitute \( y = -1 \) back into the equation \( x = 5y + 3 \):
\[ x = 5(-1) + 3 \] \[ x = -5 + 3 \] \[ x = -2 \]
Thus, the solution to the system is \( (x, y) = (-2, -1) \).
So, the intersection point is (-2, -1).