Consider the system:
9x-6y=78
-4y-14x=-68
Find X
I have attempted to work through the problem three times, and am having difficulty knowing exactly what to do. Thank you for your help. c:
9 x - 6 y = 78
14x + 4 y = 68
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18x - 12y = 156
42x + 12y = 204
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60 x = 360
x = 6
9*6 -6y = 78
54 -78 = 6y
-24 = 6 y
y = -4
Thank you. :D
To solve this system of equations, you can use the method of substitution or the method of elimination. Let's use the method of elimination in this case.
Step 1: Multiply the first equation by -2 and the second equation by -3 to make the coefficients of x in both equations opposite in sign:
-2(9x - 6y) = -2(78)
3(-4y - 14x) = 3(-68)
Simplifying these equations, we get:
-18x + 12y = -156 (equation 1)
-12y - 42x = -204 (equation 2)
Step 2: Add equation 1 and equation 2 together:
(-18x + 12y) + (-12y - 42x) = -156 + (-204)
Simplifying the left side and the right side of the equation, we get:
-18x - 42x + 12y - 12y = -360
Combining like terms, we have:
-60x = -360
Step 3: Divide both sides of the equation by -60:
-60x / -60 = -360 / -60
Simplifying:
x = 6
Therefore, the value of x in this system of equations is 6.
Remember that this is just one possible solution method, and depending on the context or personal preference, you can also choose to solve the system using the method of substitution or other methods.