Question

What is the solution of the system X - 3y = -13 and 5x + 7y = 34

Answer 1

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