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danielgeyfman

Answer:

[tex]x=3, y=-1[/tex]

Step-by-step explanation:

We know that [tex]lcm(7, 2)=14[/tex], so we need to multiply equation [tex]1[/tex] by [tex]2[/tex].

This gives [tex]2(4x-7y)=2(19)[/tex], which simplifies to [tex]8x-14y=38[/tex].

We know that [tex]lcm(2, 7)=14[/tex], so we need to multiply equation [tex]2[/tex] by [tex]7[/tex].

This gives [tex]7(3x-2y)=7(11)[/tex], which simplifies to [tex]21x-14y=77[/tex].

Aha! Now we have a path to the solution!

We can subtract the first equation from the second to eliminate [tex]y[/tex].

This gives [tex](21x-14y)-(8x-14y)=(77)-(38)[/tex], which simplifies to [tex]13x=39[/tex].

We can then divide by [tex]3[/tex] to obtain [tex]x=3[/tex]!

Then, we plug [tex]x=3[/tex] into the second equation to get [tex]3(3)-2y=11[/tex].

We can subtract [tex]9[/tex] from both sides to get [tex]-2y=2[/tex].

We then divide by [tex]-2[/tex] to obtain [tex]y=-1[/tex].

So, [tex]x=3[/tex] and [tex]y=-1[/tex], and we're done!

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