Question

3x+9y=75
8x+5y=67
what is x and y?

Answer 1

There are many ways to solve simultaneous linear equations. One of my favorite for finding integer solutions is graphing. The attached graph shows the solution to be ...

... (x, y) = (4, 7)

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You can also use Cramer's Rule, or the Vedic math variation of it, which tells you the solution to

`ax+by=c\\dx+ey=f`

is given by

`x=(bf-ec)/(\Delta)\\\\y=(cd-fa)/(\Delta)\qquad\text{where $\Delta=bd-ea$}`

Here, that means

... x = (9·67-5·75)/(9·8-5·3) = 228/57 = 4

... y = (75·8-67·3)/57 = 399/57 = 7

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A (graphing) calculator greatly facilitates either of these approaches.