((1/2) * x - 12) / ((1/2) * y - 18) = 1/7 -- Equation 1
((1/2) * x - 12) / ((1/2) * y - 18) = 1/4 -- Equation 2
Solver for x
Combining the two equations, we have:
(1/2)x - 12 = (1/7)((1/2)y - 18) [from equation 1]
(1/2)x - 12 = (1/4)((1/2)y - 18) [from equation 2]
Simplifying the right-hand side of both equations:
(1/2)x - 12 = (1/14)y - 18/7
(1/2)x - 12 = (1/8)y - 9/4
Setting the two right-hand sides equal to each other:
(1/14)y - 18/7 = (1/8)y - 9/4
Multiplying both sides by the least common multiple of the denominators (56) to clear fractions:
4y - 144 = 7y - 126
Solving for y:
3y = 18
y = 6
Substituting y = 6 into either equation 1 or 2:
(1/2)x - 12 = (1/7)((1/2)(6) - 18)
(1/2)x - 12 = -24
(1/2)x = -12
x = -24
Therefore, the solution is x = -24 and y = 6.
To solve for x, we can start by equating the two equations to each other:
(1/2 * x - 12) / (1/2 * y - 18) = 1/7 -- Equation 1
(1/2 * x - 12) / (1/2 * y - 18) = 1/4 -- Equation 2
This means that the right side of Equation 1 is equal to the right side of Equation 2.
1/7 = 1/4
To solve for x, we can cross-multiply:
(1/7) * (1/4) = (1/2 * x - 12) / (1/2 * y - 18)
Multiplying the fractions on the left, we get:
1/28 = (1/2 * x - 12) / (1/2 * y - 18)
Now, we can cross-multiply again:
1/28 * (1/2 * y - 18) = 1/2 * x - 12
Applying distributive property to the left side:
(1/56 * y - 9/2) = 1/2 * x - 12
Next, let's isolate x:
1/2 * x = (1/56 * y - 9/2) + 12
To simplify, we can find a common denominator for the right side:
1/2 * x = (1/56 * y - 9/2) + (12 * 2/2)
1/2 * x = (1/56 * y - 9/2) + 24/2
1/2 * x = (1/56 * y - 9/2) + 24/2
1/2 * x = (1/56 * y + 15/2)
Finally, we can isolate x by multiplying both sides by 2:
x = 2 * (1/56 * y + 15/2)
x = 1/28 * y + 15
So the solution for x is x = 1/28 * y + 15.