Solve the set by substitution method

It'd be easier to multiply the first equation by 3 and the second by 2 then subtract the 2nd equation from the 1st to get one equation in terms of y, but since you said it had to be the substitution method here goes:

$$2x-\frac{y+2}{2} = 22 \\ 2x = 22+\frac{y+2}{2} \\ x=11+\frac{y+2}{4}$$

Now Substituting x into the other Equation:

$$3[11+\frac{y+2}{4}] + \frac{y+2}{3} = 7 \\ 99+\frac{9(y+2)}{4}+y+2 = 21 \\ 396+9y+18+4y+8=84\\13y=-338\\y=-26\\x=11+\frac{-26+2}{4}\\
x=5$$

Rearrange the first equation to get x = (y+2)/4 + 11

 

Put this into the second equation

3*(y+2)/4 + 3*11 + (y+2)/3 = 7

 

Multiply through by 4*3

9*(y+2) +12*3*11 + 4*(y+2) = 12*7

So

9y + 18 + 396 + 4y + 8 = 84

13y + 422 = 84

13y = -338

y = -26

 

Put this back into the first equation above

x = (-26+2)/4 + 11

x = 5

 

You should check these by putting them back into the original equations.

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