Solve the equation 3n+4y=6 and 2n+3y=5

Answer 1

To solve this system of equations, we can use the method of substitution or the method of elimination. We will use the method of substitution.

From the second equation, we can isolate n:

2n + 3y = 5
2n = 5 - 3y
n = (5 - 3y)/2

Substitute this expression for n into the first equation:

3n + 4y = 6
3((5 - 3y)/2) + 4y = 6
(15 - 9y)/2 + 4y = 6
15 - 9y + 8y = 12
15 - y = 12
y = 15 - 12
y = 3

Now substitute the value of y back into the second equation to find n:

2n + 3(3) = 5
2n + 9 = 5
2n = 5 - 9
2n = -4
n = -2

Therefore, the solution to the system of equations is n = -2 and y = 3.