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. (1 point) The intersection point is (). please

Answer 1

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

1. \( x - 5y = 7 \)
2. \( 3x - 2y = -4 \)

we will solve these equations simultaneously.

Step 1: Solve the first equation for \( x \).

From equation 1:

\[ x - 5y = 7 \implies x = 5y + 7 \]

Step 2: Substitute \( x \) in the second equation.

Substituting \( x \) from equation 1 into equation 2:

\[ 3(5y + 7) - 2y = -4 \]

Expanding it:

\[ 15y + 21 - 2y = -4 \]

Combining like terms:

\[ 13y + 21 = -4 \]

Step 3: Solve for \( y \).

Subtracting 21 from both sides:

\[ 13y = -4 - 21 \] \[ 13y = -25 \]

Dividing both sides by 13:

\[ y = -\frac{25}{13} \]

Step 4: Substitute \( y \) back to find \( x \).

Now substitute \( y = -\frac{25}{13} \) back into \( x = 5y + 7 \):

\[ x = 5\left(-\frac{25}{13}\right) + 7 \] \[ x = -\frac{125}{13} + \frac{91}{13} = -\frac{125 - 91}{13} = -\frac{34}{13} \]

Step 5: State the solution.

The solution to the system of equations (the intersection point) is:

\[ \left(-\frac{34}{13}, -\frac{25}{13}\right) \]

Thus, the intersection point is \( \left(-\frac{34}{13}, -\frac{25}{13}\right) \).