Question

Choose a method to solve the linear system. Explain your choice, and then solve the system. $$ \begin{aligned} &3 y+4 x=5\\\ &x+y=1 \end{aligned} $$

Short answer

Solution to the system of equations is \(x = 0\), \(y = 1\).

Step-by-step solution

Rearrange One Equation

It's seen that the second equation, \(x + y = 1\), could easily be rearranged into \(x = 1 - y\).

Substitute into Other Equation

Now that an equation for x has been obtained, substitute \(x\) in the first equation \(3y + 4x = 5\), with the equation obtained in step 1. Obtaining \(3y + 4(1 - y) = 5\).

Solve for y

Solve the equation obtained in step 2 for \(y\), simplifying the equation gives - \(y = 1\).

Substitute Back to Obtain x

Substitute \(y = 1\) into \(x = 1 - y\), which was rearranged in step 1.

Solve for x

Solving for \(x\), we get \(x = 0\).