We are given a system of two linear equations with two variables, $x$ and $y$: $4x - 5y = -10$ $7x - 5y = 5$ We need to find the values of $x$ and $y$ that satisfy both equations.

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$:

$4x - 5y = -10$

$7x - 5y = 5$

We need to find the values of $x$ and $y$ that satisfy both equations.

2. Solution Steps

We can use the elimination method to solve the system of equations. Since the coefficient of $y$ is the same in both equations ($-5$), we can subtract the first equation from the second equation to eliminate $y$.

Equation 1: $4x - 5y = -10$

Equation 2: $7x - 5y = 5$

Subtracting Equation 1 from Equation 2:

$(7x - 5y) - (4x - 5y) = 5 - (-10)$

$7x - 5y - 4x + 5y = 5 + 10$

$3x = 15$

Divide both sides by 3 to solve for $x$:

$x = \frac{15}{3}$

$x = 5$

Now that we have the value of $x$, we can substitute it into either Equation 1 or Equation 2 to solve for $y$. Let's use Equation 1:

$4x - 5y = -10$

$4(5) - 5y = -10$

$20 - 5y = -10$

Subtract 20 from both sides:

$-5y = -10 - 20$

$-5y = -30$

Divide both sides by $-5$ to solve for $y$:

$y = \frac{-30}{-5}$

$y = 6$

Therefore, the solution to the system of equations is $x = 5$ and $y = 6$.

3. Final Answer

$x=5, y=6$