Solving a System of Equations with Common Coefficients
To solve the system of equations, let's take a look at both equations:
1. 4x - 2y = -6
2. 4x + y = -1
If we try to solve this system using elimination or substitution, we notice that both equations have the same coefficient for x, which is 4. This gives us a clue that we can subtract the second equation from the first to eliminate x and solve for y.
Performing the subtraction, we get:
(4x - 2y) - (4x + y) = -6 - (-1)
This simplifies to:
-3y = -5
Solving for y gives us:
y = -5 / -3
y = 5/3
Now, let's substitute y back into the second equation to solve for x:
4x + y = -1
4x + 5/3 = -1
To solve for x, we must get a common denominator for the terms:
4x + 5/3 = -3/3
Now, isolate 4x:
4x = -3/3 - 5/3
4x = -8/3
Divide by 4 to solve for x:
x = (-8/3) / 4
x = (-8/3) * (1/4)
x = -8/12
x = -2/3
Now we have solved for both x and y:
x = -2/3
y = 5/3
The solution to the system of equations is (-2/3, 5/3), which corresponds to the first option in the list provided.
