Solve for variable 'x' in the given system of equations:
32.
$\begin{array}{l} x - 4 y = - 20 \\ 8 x - 3 y = - 15 \end{array}$

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Answer

Final Answer: $0$

Steps

Step 1 ：Given the system of equations: $\begin{array}{l} x - 4 y = - 20 8 x - 3 y = - 15 \end{array}$

Step 2 ：First, multiply the first equation by 8 and the second equation by 1 to make the coefficients of 'x' in both equations equal.

Step 3 ：This gives us: $\begin{array}{l} 8 x - 32 y = - 160 8 x - 3 y = - 15 \end{array}$

Step 4 ：Subtract the second equation from the first to eliminate 'x' and solve for 'y'.

Step 5 ：This gives us: $29 y = - 145$ , so $y = - 145 / 29 = 5$

Step 6 ：Substitute $y = 5$ into the first equation to find the value of 'x'.

Step 7 ：This gives us: $x - 4 * 5 = - 20$ , so $x = - 20 + 20 = 0$

Step 8 ：The solution to the system of equations is $x = 0$ and $y = 5$ .

Step 9 ：Final Answer: $0$