Question

$$ \begin{aligned} &u-v=0\\\ &7 u+v=0 \end{aligned} $$

Short answer

The solution to the system of equations is \(u = 0\) and \(v = 0\).

Step-by-step solution

Solve the first equation for a variable

Given the first equation, \(u - v = 0\), it can be figured out that \(u = v\).

Substitute the value from step 1 into the second equation

The second equation is \(7u + v = 0\). Substitute \(u = v\) from Step 1 into this equation, it becomes \(7v + v = 0\), which simplifies to \(8v = 0\).

Solve for v

To get the value for \(v\), divide both sides by 8: \(v = \frac{0}{8} = 0\).

Substitute the value of v into the first equation to find u

Substituting \(v = 0\) into the first equation \(u = v\) results in \(u = 0\).