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Solve the system by the method of your choice. Identify inconsistent systems and systems with dependent equations, using set notation to express solution sets

Solve The System By The Method Of Your Choice Identify Inconsistent Systems And Systems With Dependent Equations Using Set Notation To Express Solution Sets class=

Sagot :

The given system of equations is

[tex]\begin{gathered} y=3x+5\rightarrow(1) \\ 5x-2y=-7\rightarrow(2) \end{gathered}[/tex]

Substitute y in equation (2) by equation (1)

[tex]5x-2(3x+5)=-7[/tex]

Simplify the left side

[tex]\begin{gathered} 5x-2(3x)-2(5)=-7 \\ 5x-6x-10=-7 \end{gathered}[/tex]

Add the like terms on the left side

[tex]\begin{gathered} (5x-6x)-10=-7 \\ -x-10=-7 \end{gathered}[/tex]

Add 10 to both sides

[tex]\begin{gathered} -x-10+10=-7+10 \\ -x=3 \end{gathered}[/tex]

Divide both sides by -1

[tex]\begin{gathered} \frac{-x}{-1}=\frac{3}{-1} \\ x=-3 \end{gathered}[/tex]

Substitute x in equation (1) by -3 to find y

[tex]\begin{gathered} y=3(-3)+5 \\ y=-9+5 \\ y=-4 \end{gathered}[/tex]

The solution of the system of equations is {(-3, -4)}

Since the system has only one solution then it is an independent consistent system.

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