Question

Solve the system of equations by using substitution. 6r + 7s = –12r + 4s = –12 1) (–4, –8)2) (–8, –4)3) (–7, 8)4) (8, –7)

Answer 1

Solving the system of equations by using substitution, we have:

6r + 7s = –1 Equation(1)

2r + 4s = –12 Equation(2)

6r= -1 - 7s (Subtracting 7s from both sides of equation 1)

r= -1/6 - (7/6)s (Dividing by 6 on both sides of the equation 1)

Replacing r=-1/6 - (7/6)s in equation 2 we have:

$\begin{gathered} 2(\frac{-1}{6}-\frac{7}{6}s)+4s=-12 \\ (\frac{-2}{6}-\frac{14}{6}s)+4s=-12\text{ (Distributing)} \\ \frac{-2}{6}-\frac{14}{6}s+4s=-12\text{ (Removing the parentheses}) \\ \frac{-2}{6}-\frac{14}{6}s+\frac{24}{6}s=-12(\text{ Converting 4 to a fraction with denominator 6)} \\ \frac{-2}{6}+\frac{10}{6}s=-12\text{ (Subtracting like fractions)} \\ -2+10s=-72\text{ (Multiplying by 6 on both sides of the equation)} \\ 10s=-70\text{ (Adding 2 to both sides of the equation)} \\ s=-7\text{ (Dividing on both sides of the equation by 10)} \\ s=-7 \end{gathered}$

Replacing s=-7 in the equation r= -1/6 - (7/6)s , we have:

$\begin{gathered} r=\frac{-1}{6}-\frac{7}{6}(-7)\text{ } \\ r=\frac{-1}{6}+\frac{49}{6}(\text{Multiplying)} \\ r=\frac{48}{6}(\text{Adding like fractions)} \\ r=8(\text{ Simplifying)} \end{gathered}$

The solution of the sytem of equations is: r=8 and s=-7