{:[5.2 s+0.1 r=0],[0.7(r+0.2)+3.2=-3s]:} If (r,s) is the solution to the system of equations, what is the value of s-r ?

Equation 1: We have the system of equations: 5.2s + 0.1r = 0 0.7(r + 0.2) + 3.2 = -3s Let's solve the first equation for r.Expressing r in terms of s: From the first equation, we can express r in terms of s: 0.1r = -5.2s r = -52sSubstituting r into Equation 2: Now let's substitute r = -52s into the second equation: 0.7(-52s + 0.2) + 3.2 = -3sDistributing and combining terms: Distribute 0.7 into the parentheses: 0.7 * -52s + 0.7 * 0.2 + 3.2 = -3s -36.4s + 0.14 + 3.2 = -3sIsolating s: Combine like terms: -36.4s + 3.34 = -3sSolving for s: Add 36.4s to both sides to isolate s: 3.34 = 33.4sCalculating r: Divide both sides by 33.4 to solve for s: s = 3.34 / 33.4Calculating s - r: Calculate the value of s: s = 0.1Final answer: Now that we have the value of s, let's find r using r = -52s: r = -52 * 0.1Calculate the value of r: r = -5.2Finally, calculate s - r: s - r = 0.1 - (-5.2)Perform the subtraction: s - r = 0.1 + 5.2Calculate the final answer: s - r = 5.3

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5.2 s+0.1 r=0

\newline

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

\newline

(r, s)

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

s-r

Equation $1$ : We have the system of equations: $\newline$ $5.2s + 0.1r = 0$ $\newline$ $0.7(r + 0.2) + 3.2 = -3s$ $\newline$ Let's solve the first equation for $r$ .
Expressing $r$ in terms of $s$ : From the first equation, we can express $r$ in terms of $s$ : $0.1r = -5.2s$ $r = -52s$
Substituting $r$ into Equation $2$ : Now let's substitute $r = -52s$ into the second equation: $\newline$ $0.7(-52s + 0.2) + 3.2 = -3s$
Distributing and combining terms: Distribute $0.7$ into the parentheses: $\newline$ $0.7 \times -52s + 0.7 \times 0.2 + 3.2 = -3s$ $\newline$ $-36.4s + 0.14 + 3.2 = -3s$
Isolating $s$ : Combine like terms: $\newline$ $-36.4s + 3.34 = -3s$
Solving for $s$ : Add $36.4s$ to both sides to isolate $s$ : $3.34 = 33.4s$
Calculating r: Divide both sides by $33.4$ to solve for $s$ : $\newline$ $s = \frac{3.34}{33.4}$
Calculating $s - r$ : Calculate the value of $s$ : $s = 0.1$
Final answer: Now that we have the value of $s$ , let's find $r$ using $r = -52s$ : $r = -52 \times 0.1$
Final answer: Now that we have the value of $s$ , let's find $r$ using $r = -52s$ :
$r = -52 \times 0.1$ Calculate the value of $r$ :
$r = -5.2$
Final answer: Now that we have the value of $s$ , let's find $r$ using $r = -52s$ :
$r = -52 \times 0.1$ Calculate the value of $r$ :
$r = -5.2$ Finally, calculate $s - r$ :
$s - r = 0.1 - (-5.2)$
Final answer: Now that we have the value of $s$ , let's find $r$ using $r = -52s$ :
$r = -52 \times 0.1$ Calculate the value of $r$ :
$r = -5.2$ Finally, calculate $s - r$ :
$s - r = 0.1 - (-5.2)$ Perform the subtraction:
$s - r = 0.1 + 5.2$
Final answer: Now that we have the value of $s$ , let's find $r$ using $r = -52s$ :
$r = -52 \times 0.1$ Calculate the value of $r$ :
$r = -5.2$ Finally, calculate $s - r$ :
$s - r = 0.1 - (-5.2)$ Perform the subtraction:
$s - r = 0.1 + 5.2$ Calculate the final answer:
$s - r = 5.3$