solve by substitution
(3/7)x + (5/9)y = 27
(1/9)x + (2/7)y = 7
To solve the system of equations using the substitution method, we'll solve one equation for one variable and substitute that expression into the other equation.
Let's solve the second equation for x:
(1/9)x + (2/7)y = 7
Multiply both sides of the equation by 9 to eliminate the fraction:
9 * ((1/9)x + (2/7)y) = 9 * 7
x + (18/7)y = 63/7
Next, we can express x in terms of y:
x = (63/7) - (18/7)y
x = (63 - 18y)/7
Now substitute this expression for x into the first equation:
(3/7)x + (5/9)y = 27
(3/7) * ((63 - 18y)/7) + (5/9)y = 27
Multiply through by 7 and 9 to eliminate the fractions:
3(63 - 18y) + 7(5y) = 27 * 7 * 9
189 - 54y + 35y = 567
Combine like terms:
-19y + 189 = 567
Subtract 189 from both sides:
-19y = 378
Divide both sides by -19 to solve for y:
y = 378 / -19
y = -18
Now, substitute the value of y back into the expression we found for x earlier:
x = (63 - 18(-18))/7
x = (63 + 324)/7
x = 387/7
x = 55.2857 (rounded to 4 decimal places)
Therefore, the solution to the system of equations is x = 55.2857 and y = -18.