Solve the system of equations: 5x + 4y - 14 = 0 x + 2y - 4 = 0

Let's solve the system of equations step by step:

The given system of equations is:

$$ \begin{cases} 5x + 4y - 14 = 0 \\ x + 2y - 4 = 0 \end{cases} $$

First, we can rewrite the equations as:

$$ \begin{cases} 5x + 4y = 14 \\ x + 2y = 4 \end{cases} $$

We can solve this system using substitution or elimination. Let's use elimination. Multiply the second equation by -2:

$$(-2)(x + 2y) = (-2)(4)$$ $$-2x - 4y = -8$$

Now we have the system:

$$ \begin{cases} 5x + 4y = 14 \\ -2x - 4y = -8 \end{cases} $$

Add the two equations to eliminate ( y ):

$$(5x + 4y) + (-2x - 4y) = 14 + (-8)$$ $$3x = 6$$

Divide by 3 to solve for ( x ):

$$x = \frac{6}{3} = 2$$

Now that we have ( x = 2 ), substitute it into one of the original equations to solve for ( y ). Let's use the second equation:

$$x + 2y = 4$$ $$2 + 2y = 4$$

Subtract 2 from both sides:

$$2y = 4 - 2$$ $$2y = 2$$

Divide by 2 to solve for ( y ):

$$y = \frac{2}{2} = 1$$

So the solution to the system of equations is ( x = 2 ) and ( y = 1 ).

Answer: x = 2, y = 1