9
4a + 5b - 6c = 2
-3a - 2b + 7c = -15
-a + 4b + 2c = -13

Question

Accepted Answer

# Explanation:
## Step1: Eliminate $a$ from first two equations
Multiply the first equation $4a + 5b - 6c = 2$ by $3$ and the second equation $-3a - 2b + 7c = -15$ by $4$, then add them:
$$
\begin{align*}
3(4a + 5b - 6c) + 4(-3a - 2b + 7c) &= 3\times2 + 4\times(-15)\
12a + 15b - 18c - 12a - 8b + 28c &= 6 - 60\
7b + 10c &= -54 \quad (Equation\ 4)
\end{align*}
$$
## Step2: Eliminate $a$ from second and third equations
Multiply the third equation $-a + 4b + 2c = -13$ by $-3$ and add to the second equation $-3a - 2b + 7c = -15$:
$$
\begin{align*}
-3(-a + 4b + 2c) + (-3a - 2b + 7c) &= -3\times(-13) + (-15)\
3a - 12b - 6c - 3a - 2b + 7c &= 39 - 15\
-14b + c &= 24 \quad (Equation\ 5)
\end{align*}
$$
## Step3: Solve for $b$ and $c$
From Equation 5, we have $c = 14b + 24$. Substitute into Equation 4:
$$
\begin{align*}
7b + 10(14b + 24) &= -54\
7b + 140b + 240 &= -54\
147b &= -294\
b &= -2
\end{align*}
$$
Substitute $b = -2$ into $c = 14b + 24$: $c = 14\times(-2) + 24 = -28 + 24 = -4$
## Step4: Solve for $a$
Substitute $b = -2$ and $c = -4$ into the first equation $4a + 5b - 6c = 2$:
$$
\begin{align*}
4a + 5\times(-2) - 6\times(-4) &= 2\
4a - 10 + 24 &= 2\
4a + 14 &= 2\
4a &= -12\
a &= -3
\end{align*}
$$
# Answer:
$a = -3$, $b = -2$, $c = -4$

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QUESTION IMAGE

Question

Explanation:

Step1: Eliminate \(a\) from first two equations

Step2: Eliminate \(a\) from second and third equations

Step3: Solve for \(b\) and \(c\)

Step4: Solve for \(a\)

Answer: