Question

Solve the linear system. $$\begin{array}{l}y=4 x \\\x+y=10\end{array}$$

Short answer

The solution to the given system of equations is \( x = 2 \) and \( y = 8 \).

Step-by-step solution

Substitution

Given the equations of the system, since \( y = 4x \) is already solved for y, we can substitute \( y \) in the second equation \( x + y = 10 \) with \( 4x \). Thus, the second equation after substitution will become \( x + 4x = 10 \).

Solve for x

Now, simplify the equation and solve for \( x \). The equation simplifies to \( 5x = 10 \). Dividing both sides by 5, we obtain \( x = 2 \).

Back substitution

Now, to find the value of \( y \), plug \( x = 2 \) back into the first equation \( y = 4x \). This gives us \( y = 4 * 2 \) which results in \( y = 8 \).