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Sagot :
Certainly! Let's solve the given system of equations step-by-step:
The system of equations is:
[tex]\[ \begin{cases} 12x + y = 14 \quad &\text{(1)} \\ 6x - 2 = 58 \quad &\text{(2)} \end{cases} \][/tex]
First, we need to simplify equation (2):
[tex]\[ 6x - 2 = 58 \][/tex]
Add 2 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 6x = 58 + 2 \][/tex]
[tex]\[ 6x = 60 \][/tex]
Now, divide both sides by 6 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{60}{6} \][/tex]
[tex]\[ x = 10 \][/tex]
Next, we substitute [tex]\(x = 10\)[/tex] into equation (1) to find [tex]\(y\)[/tex]:
[tex]\[ 12x + y = 14 \][/tex]
Substitute [tex]\(x = 10\)[/tex] into the equation:
[tex]\[ 12(10) + y = 14 \][/tex]
[tex]\[ 120 + y = 14 \][/tex]
Subtract 120 from both sides to solve for [tex]\(y\)[/tex]:
[tex]\[ y = 14 - 120 \][/tex]
[tex]\[ y = -106 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ x = 10 \quad \text{and} \quad y = -106 \][/tex]
Thus, the solution is [tex]\((10, -106)\)[/tex].
The system of equations is:
[tex]\[ \begin{cases} 12x + y = 14 \quad &\text{(1)} \\ 6x - 2 = 58 \quad &\text{(2)} \end{cases} \][/tex]
First, we need to simplify equation (2):
[tex]\[ 6x - 2 = 58 \][/tex]
Add 2 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 6x = 58 + 2 \][/tex]
[tex]\[ 6x = 60 \][/tex]
Now, divide both sides by 6 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{60}{6} \][/tex]
[tex]\[ x = 10 \][/tex]
Next, we substitute [tex]\(x = 10\)[/tex] into equation (1) to find [tex]\(y\)[/tex]:
[tex]\[ 12x + y = 14 \][/tex]
Substitute [tex]\(x = 10\)[/tex] into the equation:
[tex]\[ 12(10) + y = 14 \][/tex]
[tex]\[ 120 + y = 14 \][/tex]
Subtract 120 from both sides to solve for [tex]\(y\)[/tex]:
[tex]\[ y = 14 - 120 \][/tex]
[tex]\[ y = -106 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ x = 10 \quad \text{and} \quad y = -106 \][/tex]
Thus, the solution is [tex]\((10, -106)\)[/tex].
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