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]
