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x = 2, y = 7

Step-by-step explanation:

Express both ratios in fractional form, that is

= ( cross- multiply )

7(x + 1) = 3y ← distribute left side

7x + 7 = 3y ( subtract 7x from both sides )

3y - 7x = 7 → (1)

and

= ( cross- multiply )

2(y + 3) = 10x

2y + 6 = 10x ( subtract 10x from both sides )

2y - 10x + 6 = 0 ( subtract 6 from both sides )

2y - 10x = - 6 → (2)

Solve the 2 equations simultaneously\

Multiplying (1) by 2 and (2) by - 3 then adding will eliminate y

6y - 14x = 14 → (3)

- 6y + 30x = 18 → (4)

Add (3) and (4) term by term to eliminate y, that is

16x = 32 ( divide both sides by 16 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (2)

2y - 10(2) = - 6

2y - 20 = - 6 ( add 20 to both sides )

2y = 14 ( divide both sides by 2 )

y = 7

Thus x = 2 and y = 7

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step-by-step explanation:

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