$5.2 s+0.1 r=0$ $\newline$ $0.7(r+0.2)+3.2=-3s$ $\newline$ If $(r,s)$ is the solution to the system of equations, what is the value of $s-r$ ? $\newline$ $\square$

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Algebra 2

Composition of linear functions: find a value

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5.2 s+0.1 r=0

\newline

0.7(r+0.2)+3.2=-3s

\newline

(r,s)

is the solution to the system of equations, what is the value of

s-r

\newline

\square

Write down equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $5.2s + 0.1r = 0$ $\newline$ $0.7(r + 0.2) + 3.2 = -3s$
Simplify second equation: Simplify the second equation. $\newline$ Expand the term $0.7(r + 0.2)$ in the second equation: $\newline$ $0.7r + 0.7 \times 0.2 + 3.2 = -3s$ $\newline$ $0.7r + 0.14 + 3.2 = -3s$ $\newline$ Combine like terms: $\newline$ $0.7r + 3.34 = -3s$
Isolate $r$ in first equation: Isolate $r$ in the first equation. $\newline$ From the first equation, we can express $r$ in terms of $s$ : $\newline$ $0.1r = -5.2s$ $\newline$ $r = (-5.2s) / 0.1$ $\newline$ $r = -52s$
Substitute $r$ into second equation: Substitute the expression for $r$ from Step $3$ into the second equation. $\newline$ Replace $r$ with $-52s$ in the second equation: $\newline$ $0.7(-52s) + 3.34 = -3s$ $\newline$ $-36.4s + 3.34 = -3s$
Solve for s: Solve for s. $\newline$ Add $36.4s$ to both sides of the equation to isolate $s$ : $\newline$ $-36.4s + 36.4s + 3.34 = -3s + 36.4s$ $\newline$ $3.34 = 33.4s$ $\newline$ Divide both sides by $33.4$ to find $s$ : $\newline$ $s = \frac{3.34}{33.4}$ $\newline$ $s = 0.1$
Substitute $s$ into $r$ : Substitute the value of $s$ back into the expression for $r$ from Step $3$ . $\newline$ $r = -52s$ $\newline$ $r = -52 \times 0.1$ $\newline$ $r = -5.2$
Calculate $s - r$ : Calculate $s - r$ . $\newline$ $s - r = 0.1 - (-5.2)$ $\newline$ $s - r = 0.1 + 5.2$ $\newline$ $s - r = 5.3$