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A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 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.

(1 point)
The intersection point is (
).
Remaining Attempts : 3
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1 answer

To find the solution to the system of equations given by \( x - 5y = 7 \) and \( 3x - 2y = -4 \), we need to solve these equations simultaneously.

  1. First equation: Rearranging \( x - 5y = 7 \): \[ x = 5y + 7 \]

  2. Substituting in the second equation: Substitute \( x \) into \( 3x - 2y = -4 \): \[ 3(5y + 7) - 2y = -4 \] Simplifying: \[ 15y + 21 - 2y = -4 \] \[ 13y + 21 = -4 \] \[ 13y = -4 - 21 \] \[ 13y = -25 \] \[ y = -\frac{25}{13} \]

  3. Finding \( x \): Now substitute \( y \) back into the rearranged first equation: \[ x = 5\left(-\frac{25}{13}\right) + 7 \] \[ x = -\frac{125}{13} + \frac{91}{13} \] \[ x = -\frac{125 - 91}{13} = -\frac{34}{13} \]

So the intersection point (the solution to the system of equations) is: \[ \left( -\frac{34}{13}, -\frac{25}{13} \right) \] Thus, the answer to fill in the blank is:

The intersection point is \((- \frac{34}{13}, -\frac{25}{13})\).