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

Solve By The Method Of Your Choice Identify Systems With No Solution And Systems With Infinitely Many Solutions class=

Sagot :

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).

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