Answer:
Explanation:
To solve the system of linear equations using the addition/elimination method, you can start by multiplying one or both equations by appropriate constants to make it easier to eliminate one of the variables. In this case, you can eliminate the variable "x" by multiplying the second equation by 3 so that the coefficients of "x" in both equations become equal:
The original equations are:
3x + 11y = 4
-2x - 6y = 0
Now, multiply the second equation by 3:
3 * (-2x - 6y) = 3 * 0
This simplifies to:
-6x - 18y = 0
Now, your system of equations looks like this:
3x + 11y = 4
-6x - 18y = 0
Now, you can add the two equations together to eliminate the variable "x":
(3x + 11y) + (-6x - 18y) = 4 + 0
Combine like terms:
(3x - 6x) + (11y - 18y) = 4
This simplifies to:
-3x - 7y = 4
Now, you have a new equation:
-3x - 7y = 4
Now, you can solve this equation for "y":
-3x - 7y = 4
Subtract -3x from both sides:
-7y = 3x + 4
Divide by -7 to isolate "y":
y = -(3x + 4) / 7
Now that you have an expression for "y" in terms of "x," you can substitute this into either of the original equations (I'll use the first one):
3x + 11y = 4
3x + 11(-3x - 4/7) = 4
Now, solve for "x":
3x - 33x - 44/7 = 4
Combine like terms:
-30x - 44/7 = 4
Add 44/7 to both sides:
-30x = 4 + 44/7
To add 4 and 44/7, you need a common denominator, which is 7:
-30x = (28/7 + 44/7)
-30x = 72/7
Now, divide by -30 to solve for "x":
x = (72/7) / -30
x = -72/210
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6:
x = -(12/35)
Now that you have the value of "x," you can use it to find "y" using the equation we derived earlier:
y = -(3x + 4) / 7
y = -(3(-12/35) + 4) / 7
y = -(-36/35 + 4) / 7
y = (36/35 - 4) / 7
To subtract 4 from 36/35, you need a common denominator, which is 35:
y = (36/35 - 140/35) / 7
y = (-104/35) / 7
Now, divide the numerator by 7:
y = -(104/35) / 7
y = -(104/35) * (1/7)
y = -(104/245)
So, the solution to the system of equations is:
x = -(12/35)
y = -(104/245)
You can simplify the fractions further if needed.