Question

solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions

Answer 1

To solve the system of equations, follow the steps below.

Step 01: Solve the first equation for x.

To do it, subtract 4 y from both sides of the equation.

`\begin{gathered} x+4y-4y=14-4y \\ x=14-4y \end{gathered}`

Step 02: Substitute x by (14 - 4y) in the second equation.

`\begin{gathered} 2x-y=1 \\ 2*(14-4y)-y=1 \end{gathered}`

Step 03: Solve the equation for y.

To do it, first, solve the multiplication and the addition.

`\begin{gathered} 28-8y-y=1 \\ 28-9y=1 \end{gathered}`

Now, subtract 28 from both sides. Then, divide the sides by -9.

`\begin{gathered} 28-9y-28=1-28 \\ -9y=-27 \\ (-9y)/(-9)=(-27)/(-9) \\ y=3 \end{gathered}`

Step 04: Substitute y by 3 and find x using the equation from step 1.

`\begin{gathered} x=14-4y \\ x=14-4*3 \\ x=14-12 \\ x=2 \end{gathered}`

Answer:

The system has one solution:

x = 2 and y = 3, which is the same as (2, 3).