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3x - 2y = -4
x - 5y = 3
Review the graphs of a system of two linear equations in two variables: x - 5y = 7 and 3x - 2y = -4. Find the solution to both equations.
The intersection point is (__).

1 answer

To find the solution to the system of linear equations given by:

  1. \( 3x - 2y = -4 \)
  2. \( x - 5y = 3 \)

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).