Final answer:
To solve the system of linear equations using the substitution method, you need to solve one equation for one variable and then substitute that expression into the other equation. In this case, solving the first equation for x, we get x = (33 - 5y)/2. Substituting this expression into the second equation, we find y = 122/21. Substituting this value of y back into the first equation, we find x = 83/42.
Step-by-step explanation:
To solve the system of linear equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation. Let's solve the first equation for x:
2x/3 + 5y/3 = 11
2x + 5y = 33
To get x alone, we isolate x:
2x = 33 - 5y
x = (33 - 5y)/2
Now we substitute this expression for x into the second equation:
5x/3 + 2y/3 = 3
5((33 - 5y)/2)/3 + 2y/3 = 3
Simplifying, we get:
(165 - 25y)/6 + 2y/3 = 3
Multiplying both sides by 6 to get rid of denominators:
(165 - 25y) + 4y = 18
Combining like terms:
140 - 21y = 18
Subtracting 140 from both sides:
-21y = -122
Dividing both sides by -21:
y = 122/21
Now we substitute this value of y back into either of the original equations to find x. Using the first equation:
2x/3 + 5(122/21)/3 = 11
Multiplying both sides by 3 to get rid of denominators:
2x + 5(122/21) = 33
Multiplying both sides by 21:
42x + 5(122) = 693
Combining like terms:
42x + 610 = 693
Subtracting 610 from both sides:
42x = 83
Dividing both side by 42:
x = 83/42
Therefore, the solution to the system of linear equations is (x, y) = (83/42, 122/21).