Answer:
x = 14, y = -2
(14, -2)
Step-by-step explanation:
The given problem involves solving systems of linear equation by substitution.
Given the equations:
Equation 1: 6(2x + 3) - y = 188
Equation 2: 4x + y = 54
Start by isolating y in Equation 2 by subtracting 4x from both sides:
4x - 4x + y = - 4x + 54
y = - 4x + 54
Next, work on Equation 1 by distributing 6 into the parenthesis:
6(2x + 3) - y = 188
12x + 18 - y = 188
Then, substitute the value of y from Equation 1 into Equation 2:
12x + 18 - y = 188
12x + 18 - (-4x + 54) = 188
Distribute -1 into (-4x + 54): ←←← This was the skipped step in the given problem, causing an erroneous solution!
12x + 18 + 4x - 54 = 188
Combine like terms:
16x - 36 = 188
Add 36 to both sides to isolate 16x:
16x - 36 + 36 = 188 + 36
16x = 224
Divide both sides by 16:
[tex]\frac{16x}{16} = \frac{224}{16}[/tex]
x = 14
Now that we have the value of x, substitute its value into Equation 2 to solve for y:
y = -4x + 54
y = -4(14) + 54
y = -56 + 54
y = -2
Therefore, the solution to the given systems of linear equation is:
x = 14, y = -2
(14, -2)
To answer your question, the error is that -1 was not properly distributed when the value of y = (-4x + 54) was substituted into Equation 1. I've included a screenshot where it shows that error.
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