3(x+y)+1=x+4y Expanding the left side, we get: 3x + 3y + 1 = x + 4y
Subtracting x from both sides: 2x + 3y + 1 = 4y
Subtracting 3y from both sides: 2x + 1 = y
Now, let's solve the second equation:
7 - 2(x-y) = x - 8y Expanding the left side, we get: 7 - 2x + 2y = x - 8y
Adding 2x to both sides: 7 + 2y = 3x - 8y
Adding 8y to both sides: 7 + 10y = 3x
Dividing by 3 on both sides: (7 + 10y) / 3 = x
Now, we have the two equations: 2x + 1 = y (7 + 10y) / 3 = x
We can substitute the value of x from the second equation into the first equation to solve for y: 2(7 + 10y) / 3 + 1 = y 14 + 20y / 3 + 1 = y 14 + 20y / 3 - 3y / 3 = y 14 + 17y / 3 = y y = 14 / 3
Now we can substitute the value of y back into the second equation to solve for x: x = (7 + 10(14 / 3)) / 3 x = (7 + 140 / 3) / 3 x = (21 + 140) / 3 x = 161 / 3
Therefore, the solution to the system of equations is: x = 161 / 3 y = 14 / 3
3(x+y)+1=x+4y
Expanding the left side, we get:
3x + 3y + 1 = x + 4y
Subtracting x from both sides:
2x + 3y + 1 = 4y
Subtracting 3y from both sides:
2x + 1 = y
Now, let's solve the second equation:
7 - 2(x-y) = x - 8y
Expanding the left side, we get:
7 - 2x + 2y = x - 8y
Adding 2x to both sides:
7 + 2y = 3x - 8y
Adding 8y to both sides:
7 + 10y = 3x
Dividing by 3 on both sides:
(7 + 10y) / 3 = x
Now, we have the two equations:
2x + 1 = y
(7 + 10y) / 3 = x
We can substitute the value of x from the second equation into the first equation to solve for y:
2(7 + 10y) / 3 + 1 = y
14 + 20y / 3 + 1 = y
14 + 20y / 3 - 3y / 3 = y
14 + 17y / 3 = y
y = 14 / 3
Now we can substitute the value of y back into the second equation to solve for x:
x = (7 + 10(14 / 3)) / 3
x = (7 + 140 / 3) / 3
x = (21 + 140) / 3
x = 161 / 3
Therefore, the solution to the system of equations is:
x = 161 / 3
y = 14 / 3