To solve these simultaneous equations using the elimination method, we need to eliminate one variable by multiplying one or both of the equations by suitable numbers so that the coefficients of either x or y will become the same or additive inverses.
Let's start by multiplying the second equation by 2 to make the coefficients of x opposite:
2 * (3x + 4y) = 2 * 16
6x + 8y = 32
Now we have:
6x - 5y = -7
6x + 8y = 32
Next, we need to eliminate the x variable. Subtract the first equation from the second equation:
(6x + 8y) - (6x - 5y) = 32 - (-7)
6x + 8y - 6x + 5y = 32 + 7
13y = 39
Dividing both sides of the equation by 13:
13y/13 = 39/13
y = 3
Now substitute the value of y into one of the original equations, let's use the first one:
6x - 5(3) = -7
6x - 15 = -7
6x = -7 + 15
6x = 8
Dividing both sides by 6:
6x/6 = 8/6
x = 4/3
So, the solution to the simultaneous equations is:
x = 4/3
y = 3