What is the y-coordinate of the solution of the system?
{3x+10y=7, x-10y=29}

We know that:

3x + 10y = 7

We also know that:

x - 10y = 29

Which means that:

x = 29 + 10y

If, x = 29 + 10y,

3(29 + 10y) + 10y = 7

3*29 + 30y + 10y = 7

3(20+9) + 40y = 7

60 + 27 + 40y = 7

87 + 40y = 7

40y = 7 - 87

40y= -80

y=(-80)/40

y=-2

Answer y=-2.

If y=-2,

x-10(-2)=29

x+20=29

x=29-20

x=9

Let's see if these results are true:

3(9)+10(-2)=7

27-20=7 (Correct)



9-10(-2)=29

9+20=29 (Correct)

Answer once again:

y=-2

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