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$0.7 a - 0.8b = -0.1\ a - 1.4 = -6(b - 0.1)$

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Solve one-step addition and subtraction equations with decimals and fractions

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Q.

0.7 a - 0.8b = -0.1\ a - 1.4 = -6(b - 0.1)

Write Equations: First, let's write down the system of equations we need to solve: $\newline$ $0.7a - 0.8b = -0.1$ $\newline$ $a - 1.4 = -6(b - 0.1)$
Simplify Second Equation: We can 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 can add $1.4$ to both sides of the second equation to isolate $a$ : $a = -6b + 0.6 + 1.4$ $a = -6b + 2$
Substitute into First Equation: Now we have an expression for $a$ in terms of $b$ . We can substitute this expression into the first equation in place of $a$ : $0.7(-6b + 2) - 0.8b = -0.1$
Distribute and Combine Terms: Distribute the $0.7$ into the parentheses: $\newline$ $-4.2b + 1.4 - 0.8b = -0.1$
Isolate Term with $b$ : Combine like terms: $-5b + 1.4 = -0.1$
Solve for $b$ : Subtract $1.4$ from both sides to isolate the term with $b$ :
$-5b = -0.1 - 1.4$
$-5b = -1.5$
Substitute $b$ into a Expression: Divide both sides by $-5$ to solve for $b$ : $b = \frac{-1.5}{-5}$ $b = 0.3$
Calculate Value of a: Now that we have the value of b, we can substitute it back into the expression we found for a: $\newline$ $a = -6(0.3) + 2$
Calculate Value of a: Now that we have the value of b, we can substitute it back into the expression we found for a: $\newline$ $a = -6(0.3) + 2$ Calculate the value of a: $\newline$ $a = -1.8 + 2$ $\newline$ $a = 0.2$

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