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.
[tex]\begin{gathered} x+4y-4y=14-4y \\ x=14-4y \end{gathered}[/tex]
Step 02: Substitute x by (14 - 4y) in the second equation.
[tex]\begin{gathered} 2x-y=1 \\ 2*(14-4y)-y=1 \end{gathered}[/tex]
Step 03: Solve the equation for y.
To do it, first, solve the multiplication and the addition.
[tex]\begin{gathered} 28-8y-y=1 \\ 28-9y=1 \end{gathered}[/tex]
Now, subtract 28 from both sides. Then, divide the sides by -9.
[tex]\begin{gathered} 28-9y-28=1-28 \\ -9y=-27 \\ \frac{-9y}{-9}=\frac{-27}{-9} \\ y=3 \end{gathered}[/tex]
Step 04: Substitute y by 3 and find x using the equation from step 1.
[tex]\begin{gathered} x=14-4y \\ x=14-4*3 \\ x=14-12 \\ x=2 \end{gathered}[/tex]
Answer:
The system has one solution:
x = 2 and y = 3, which is the same as (2, 3).
