Asked by A5ComeTrimErrTime
Solve each system of linear equation and explain any method you used:
4x+1/3y=50
-3x-8y=-84
4x+1/3y=50
-3x-8y=-84
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Answered by
GPT 3.5
To solve the system of linear equations, we can use the method of substitution or the method of elimination.
Let's use the method of substitution to solve this system:
From the first equation, we can isolate "x" by subtracting 1/3y from both sides of the equation:
4x + (1/3)y = 50
4x = 50 - (1/3)y
x = (50 - (1/3)y)/4
Now we substitute this value of "x" into the second equation:
-3x - 8y = -84
-3((50 - (1/3)y)/4) - 8y = -84
Simplifying this equation step by step:
-3(50 - (1/3)y)/4 - 8y = -84
-3(50 - (1/3)y) - 32y = -336
-150 + (1/3)y - 32y = -336
-150 - 32y + (1/3)y = -336
(1/3)y - 32y = -336 + 150
-31(1/3)y = -186
-(4/3)y = -186
y = (-186)(-3/4)
y = 279/4
y = 69.75
Now we substitute the value of "y" back into the first equation to solve for "x":
4x + (1/3)(69.75) = 50
4x + 23.25 = 50
4x = 50 - 23.25
4x = 26.75
x = 26.75/4
x = 6.6875
Therefore, the solution to the system of equations is x = 6.6875 and y = 69.75.
Let's use the method of substitution to solve this system:
From the first equation, we can isolate "x" by subtracting 1/3y from both sides of the equation:
4x + (1/3)y = 50
4x = 50 - (1/3)y
x = (50 - (1/3)y)/4
Now we substitute this value of "x" into the second equation:
-3x - 8y = -84
-3((50 - (1/3)y)/4) - 8y = -84
Simplifying this equation step by step:
-3(50 - (1/3)y)/4 - 8y = -84
-3(50 - (1/3)y) - 32y = -336
-150 + (1/3)y - 32y = -336
-150 - 32y + (1/3)y = -336
(1/3)y - 32y = -336 + 150
-31(1/3)y = -186
-(4/3)y = -186
y = (-186)(-3/4)
y = 279/4
y = 69.75
Now we substitute the value of "y" back into the first equation to solve for "x":
4x + (1/3)(69.75) = 50
4x + 23.25 = 50
4x = 50 - 23.25
4x = 26.75
x = 26.75/4
x = 6.6875
Therefore, the solution to the system of equations is x = 6.6875 and y = 69.75.
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