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Simply take the first equation and substitute it for y in the second one.

We're told:

y = -3x + 5

and:

5x - 4y = -3

So we can say:

5x - 4(-3x + 5) = -3

5x + 12x - 20 = -3

17x = 17

x = 1

Then plug that value into one of our original equations to solve for y:

y = -3x + 5

y = -3(1) + 5

y = 5 - 3

y = 2

So the two equations intersect at the point (1, 2).

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