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solve the system of equations and choose the correct ordered pair. 2x - 6y = 85x - 4y = 31

Sagot :

We have

[tex]\begin{gathered} 2x-6y=8\text{ (1)} \\ 5x-4y=31\text{ (2)} \end{gathered}[/tex]

we must solve the system of equations

First, we will solve for x the first equation

[tex]\begin{gathered} 2x-6y=8 \\ 2x=8+6y \\ x=\frac{8}{2}+\frac{6}{2}y \\ x=4+3y \end{gathered}[/tex]

Then, we must replace the value of x in the second equation

[tex]\begin{gathered} 5(4+3y)-4y=31 \\ 20+15y-4y=31 \\ 11y=11 \\ y=\frac{11}{11} \\ y=1 \end{gathered}[/tex]

Finally, we replace the value of y in the equation that we solved for x

[tex]\begin{gathered} x=4+3(1) \\ x=4+3 \\ x=7 \end{gathered}[/tex]

So, the correct ordered pair is (7, 1)

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