Question

solve the following system of equations for y: -7x + 5y = 6 5x + 2y = 5 -\frac{5}{3} \frac{5}{3} \frac{1}{3} -\frac{13}{11} multiple choice 4 points solve: 6(2x - 5) = 54 x = \frac{59}{12} x = 7 x = \frac{53}{8} x = 9 multiple choice 4 points solve: 15j + 2 = 14 \frac{11}{15} \frac{13}{17} 1 \frac{4}{5}

Explanation:

Step1: Solve the system for $y$

Multiply the first - equation $-7x + 5y=6$ by $5$ and the second - equation $5x + 2y = 5$ by $7$ to eliminate $x$.
The first equation becomes $-35x+25y = 30$.
The second equation becomes $35x+14y = 35$.
Adding these two new equations:
\[

$$\begin{align*} (-35x + 25y)+(35x+14y)&=30 + 35\\ -35x+35x+25y + 14y&=65\\ 39y&=65\\ y&=\frac{65}{39}=\frac{5}{3} \end{align*}$$

\]

Step2: Solve $6(2x - 5)=54$ for $x$

First, divide both sides of the equation by $6$:
\[2x-5=\frac{54}{6}=9\]
Then, add $5$ to both sides:
\[2x=9 + 5=14\]
Finally, divide both sides by $2$:
\[x = 7\]

Step3: Solve $15j+2 = 14$ for $j$

Subtract $2$ from both sides:
\[15j=14 - 2=12\]
Then, divide both sides by $15$:
\[j=\frac{12}{15}=\frac{4}{5}\]

Answer:

1. $\frac{5}{3}$
2. $x = 7$
3. $\frac{4}{5}$