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solve the linear system: y=6x - 11 and -2x - 3y= -7 answer will be a coordinate consisting of integers

Sagot :

Given the following system of equations:

[tex]\begin{gathered} y=6x-11 \\ -2x-3y=-7 \end{gathered}[/tex]

we can substitute the first equation on the second to find the value of x:

[tex]\begin{gathered} -2x-3(6x-11)=-7 \\ \Rightarrow-2x-18x+33=-7 \\ \Rightarrow-20x=-7-33=-40 \\ \Rightarrow x=\frac{-40}{-20}=2 \\ x=2 \end{gathered}[/tex]

Now we can find the value of y using x=2:

[tex]\begin{gathered} y=6(2)-11=12-11=1 \\ y=1 \end{gathered}[/tex]

therefore, the solution of the system is (2,1)

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