4x + 3y = -2
4x - 4y = -16
a. y=-1 b. y=-2 c. y=1 d. y=2
multiply second equation by -1 then add
+4x + 3y = -2
-4x + 4y = 16
---------------add
0 + 7 y = 14
so
= +2
-x+4x
To solve this system of equations, we can use the method of elimination. The goal is to eliminate one variable, either x or y, by adding or subtracting the two equations. Let's solve the system step by step.
Step 1: Choose one variable to eliminate.
In this case, let's eliminate x. To do that, we'll multiply both sides of the second equation by -1. This will make the coefficients of x in both equations the same.
The original equations are:
1) 4x + 3y = -2
2) 4x - 4y = -16
Multiplying the second equation by -1:
-1 * (4x - 4y) = -1 * (-16)
-4x + 4y = 16
The modified equations are now:
1) 4x + 3y = -2
3) -4x + 4y = 16
Step 2: Add the equations to eliminate x.
Now, we'll add equation 1 and 3 to eliminate x.
(4x + 3y) + (-4x + 4y) = (-2) + 16
Simplifying the equation:
4x - 4x + 3y + 4y = 14y = 14
So, the solution is y = 14.
Step 3: Substitute the value of y back into one of the original equations to find the value of x.
Let's substitute y = 14 into equation 1:
4x + 3(14) = -2
4x + 42 = -2
4x = -2 - 42
4x = -44
x = -44 / 4
x = -11
Therefore, the solution to this system of equations is x = -11 and y = 14.
Comparing the given options, the correct answer is: d. y = 2.