Question - Solving a System of Equations with Common Coefficients
Solution:
To solve the system of equations, let's take a look at both equations:1. 4x - 2y = -62. 4x + y = -1If 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 = -5Solving for y gives us:y = -5 / -3y = 5/3Now, let's substitute y back into the second equation to solve for x:4x + y = -14x + 5/3 = -1To solve for x, we must get a common denominator for the terms:4x + 5/3 = -3/3Now, isolate 4x:4x = -3/3 - 5/34x = -8/3Divide by 4 to solve for x:x = (-8/3) / 4x = (-8/3) * (1/4)x = -8/12x = -2/3Now we have solved for both x and y:x = -2/3y = 5/3The solution to the system of equations is (-2/3, 5/3), which corresponds to the first option in the list provided.
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