Question

Choose a method to solve the linear system. Explain your choice. $$ \begin{aligned} &3 x+5 y=25\\\ &2 x-6 y=12 \end{aligned} $$

Short answer

The short answer will be the values of x and y obtained in steps 3 and 5 respectively. They are the solution to the system of linear equations provided.

Step-by-step solution

Solve first equation for one variable

Rearrange the first equation \(3x + 5y = 25\) to solve for x: \(x = \rac{25 - 5y}{3}\)

Substitute equation obtained in step 1 into the other equation

Substitute the value of x from Step 1 into the second equation: \(2(\frac{25 - 5y}{3}) - 6y = 12\). Then, simplify it to solve for y.

Calculate the value of y

Solving the equation will give the value of y. Make sure to record this value as we'll need it for finding x.

Substitute y into first equation

Substitute the found value for y into first equation to find x: \(3x + 5*y = 25\). It should result in an equation that only contains x.

Calculate the value of x

Finally, solve the equation to find x. The values of x and y will be the solution for the given system of equations.