Question

6x–5y=27

3x+5y=36

Answer 1

To solve this system of equations, we can use the method of elimination.

First, let's multiply the second equation by 2 to make the coefficients of y in both equations opposites:

2(3x + 5y) = 2(36)
6x + 10y = 72

Now, we have:
6x - 5y = 27
6x + 10y = 72

Adding the two equations together, we eliminate the variable x:

(6x - 5y) + (6x + 10y) = 27 + 72
12x + 5y = 99

Now, we can solve for y by subtracting 12x from both sides:

5y = 99 - 12x
5y = 99 - 12x
5y = 99 - 12x
y = 19.8 - 2.4x

Next, we substitute this value of y back into one of the original equations to find x:

3x + 5(19.8 - 2.4x) = 36
3x + 99 - 12x = 36
-9x + 99 = 36
-9x = -63
x = 7

Finally, plug the value of x back into one of the original equations to solve for y:

6(7) - 5y = 27
42 - 5y = 27
-5y = -15
y = 3

Therefore, the solution to the system of equations is x = 7 and y = 3.