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$\begin{aligned} 0.7 a - 0.8b &= -0.1\ a - 1.4 &= -6(b - 0.1) \end{aligned}$

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Find values of derivatives using limits

Full solution

Q.

\begin{aligned} 0.7 a - 0.8b &= -0.1\ a - 1.4 &= -6(b - 0.1) \end{aligned}

Write Equations: First, let's write down the system of equations we need to solve: $\newline$ \begin{aligned} $\newline$ $0$ . $7$ a - $0$ . $8$ b &= $-0$ . $1$ (\newline\) a - $1$ . $4$ &= $-6$ (b - $0$ . $1$ ) $\newline$ \end{aligned}
Simplify Second Equation: We will start by simplifying the second equation. Distribute the $-6$ on the right side of the equation: $\newline$ $a - 1.4 = -6b + 0.6$
Isolate Variable $a$ : Next, we add $1.4$ to both sides of the second equation to isolate $a$ : $a = -6b + 0.6 + 1.4$
Substitute into First Equation: Now, we simplify the right side of the equation by combining like terms: $a = -6b + 2$
Distribute $0$ . $7$ : We can now substitute the expression for $a$ from the second equation into the first equation: $0.7(-6b + 2) - 0.8b = -0.1$
Combine Like Terms: Distribute the $0.7$ into the parentheses: $-4.2b + 1.4 - 0.8b = -0.1$
Correct Combination of Terms: Combine like terms by adding the coefficients of $b$ : $-4.2b - 0.8b = -1.4 - 0.1$
Correct Combination of Terms: Combine like terms by adding the coefficients of $b$ : $-4.2b - 0.8b = -1.4 - 0.1$ The correct combination of like terms should be: $-4.2b - 0.8b = -5b$ $1.4 - 0.1 = 1.3$ So the equation should be: $-5b = -1.3$

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