Answer:
The solution for this system is x = 1/2 and y = 9/2
Step-by-step explanation:
1. We have this system of equations:
x - 3y = -13 and 5x + 7y = 34
2. Let's try to find out the value of x on the first equation:
x - 3y = - 13
x = 3y - 13
3. Now, let's replace x on the second equation for finding y:
5x + 7y = 34
5 (3y - 13) + 7y = 34
15y - 65 + 7y = 34
22y = 34 +65
22y = 99
2y = 9 (Dividing by 11 at both sides)
y = 9/2 (Diving by 2 at both sides)
4. Now, let's find out the value of x on the first equation, using the value of y:
x - 3y = - 13
x - 3 (9/2) = - 13
x - 27/2 = -13
x = -13 + 27/2
x = (-26 + 27)/2 (Adding - 13 and 27/2)
x = 1/2
5. Finally, let's prove the values of x and y are correct on the second equation of the system:
5x + 7y = 34
5 (1/2) + 7 (9/2) = 34
5/2 + 63/2 = 34
(5 + 63)/2 = 34
68/2 = 34
34 = 34
It has been proved that x = 1/2 and y = 9/2 are correct
