10. ) x-4y=-5 -3x-8y=0

To solve the system of equations:<br /><br />\[<br />\begin{cases}<br />x - 4y = -5 \\<br />-3x - 8y = 0<br />\end{cases}<br />\]<br /><br />we can use either the substitution method or the elimination method. Here, I'll use the elimination method.<br /><br />First, let's eliminate \( x \) by making the coefficients of \( x \) in both equations equal. We can do this by multiplying the first equation by 3:<br /><br />1. Multiply the first equation by 3:<br /> \[<br /> 3(x - 4y) = 3(-5)<br /> \]<br /> which simplifies to:<br /> \[<br /> 3x - 12y = -15<br /> \]<br /><br />Now we have the system:<br />\[<br />\begin{cases}<br />3x - 12y = -15 \\<br />-3x - 8y = 0<br />\end{cases}<br />\]<br /><br />2. Add the two equations together to eliminate \( x \):<br /> \[<br /> (3x - 12y) + (-3x - 8y) = -15 + 0<br /> \]<br /> This simplifies to:<br /> \[<br /> -20y = -15<br /> \]<br /><br />3. Solve for \( y \):<br /> \[<br /> y = \frac{-15}{-20} = \frac{3}{4}<br /> \]<br /><br />4. Substitute \( y = \frac{3}{4} \) back into the first equation to solve for \( x \):<br /> \[<br /> x - 4\left(\frac{3}{4}\right) = -5<br /> \]<br /> Simplify:<br /> \[<br /> x - 3 = -5<br /> \]<br /> \[<br /> x = -5 + 3<br /> \]<br /> \[<br /> x = -2<br /> \]<br /><br />Thus, the solution to the system of equations is:<br />\[<br />x = -2, \quad y = \frac{3}{4}<br />\]