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Solve the following system of equations:

[tex]\[
\begin{cases}
3x + y = 8 \\
4x - y = 6
\end{cases}
\][/tex]

Sagot :

GinnyAnsweridn
To solve the system of linear equations:

[tex]\[ \begin{cases} 3x + y = 8.4 \\ 4x - y = 6 \end{cases} \][/tex]

we can follow these steps:

1. Add both equations to eliminate [tex]\(y\)[/tex]:

[tex]\[ \begin{aligned} (3x + y) + (4x - y) &= 8.4 + 6 \\ 3x + 4x + y - y &= 14.4 \\ 7x &= 14.4 \\ x &= \frac{14.4}{7} \\ x &= 2.05714285714286 \end{aligned} \][/tex]

2. Substitute the value of [tex]\(x\)[/tex] back into one of the original equations to solve for [tex]\(y\)[/tex]:

Let's use the first equation [tex]\(3x + y = 8.4\)[/tex]:

[tex]\[ \begin{aligned} 3(2.05714285714286) + y &= 8.4 \\ 6.17142857142858 + y &= 8.4 \\ y &= 8.4 - 6.17142857142858 \\ y &= 2.22857142857143 \end{aligned} \][/tex]

So, the solution to the system of equations is:

[tex]\[ x = 2.05714285714286, \quad y = 2.22857142857143. \][/tex]
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