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0.7 a-0.8 b=-0.1

a-1.4=-6(b-0.1)
Consider the system of equations. If
(a,b) is the solution to the system, then what is the value of the sum of
a and
b ?
Choose 1 answer:
(A) -0.5
(B) -0.1
(C) 0.1
(D) 0.5

$0.7 a-0.8 b=-0.1$ $\newline$ $a-1.4=-6(b-0.1)$ $\newline$ Consider the system of equations. If $(a, b)$ is the solution to the system, then what is the value of the sum of $a$ and $b$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-0$ . $5$ $\newline$ (B) $-0$ . $1$ $\newline$ (C) $0$ . $1$ $\newline$ (D) $0$ . $5$

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Solve rational equations

Full solution

Q.

0.7 a-0.8 b=-0.1

\newline

a-1.4=-6(b-0.1)

\newline

Consider the system of equations. If

(a, b)

is the solution to the system, then what is the value of the sum of

a

and

b

?

\newline

Choose

1

answer:

\newline

(A)

-0

.

5

\newline

(B)

-0

.

1

\newline

(C)

0

.

1

\newline

(D)

0

.

5

Write System Equations: Write down the system of equations. $\newline$ $0.7a - 0.8b = -0.1$ $\newline$ $a - 1.4 = -6(b - 0.1)$
Simplify Second Equation: Simplify the second equation. $\newline$ $a - 1.4 = -6b + 0.6$ $\newline$ Add $1.4$ to both sides to isolate $a$ . $\newline$ $a = -6b + 0.6 + 1.4$ $\newline$ $a = -6b + 2$
Substitute Expression for a: Substitute the expression for $a$ from the second equation into the first equation. $0.7(-6b + 2) - 0.8b = -0.1$
Distribute and Combine Terms: Distribute $0.7$ into the parentheses. $\newline$ $-4.2b + 1.4 - 0.8b = -0.1$
Isolate Term with b: Combine like terms. $\newline$ $-4.2b - 0.8b + 1.4 = -0.1$ $\newline$ $-5b + 1.4 = -0.1$
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 Second Equation: Divide both sides by $-5$ to solve for $b$ . $b = \frac{-1.5}{-5}$ $b = 0.3$
Find Sum of a and b: Substitute the value of $b$ back into the simplified second equation to solve for $a$ . $a = -6(0.3) + 2$ $a = -1.8 + 2$ $a = 0.2$
Find Sum of a and b: Substitute the value of $b$ back into the simplified second equation to solve for $a$ .
$a = -6(0.3) + 2$
$a = -1.8 + 2$
$a = 0.2$ Add the values of $a$ and $b$ to find the sum.
$a + b = 0.2 + 0.3$
$a + b = 0.5$

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