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$-24$ $-8$ j= $12$ k, $3$ +\frac{ $5$ }{ $3$ } k = -\frac{ $7$ }{ $6$ }j? which of the following ordered pairs $(j,K)$ is the solution to the systems of equations given above, $\newline$ a. $(6,-6)$ , $\newline$ b. $(3,0)$ , $\newline$ c. $(0,2)$ , $\newline$ d. $(-4,1)$

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Write linear equations in standard form

Full solution

Q.

-24

-8

j=

12

k,

3

+\frac{

5

}{

3

} k = -\frac{

7

}{

6

}j? which of the following ordered pairs

(j,K)

is the solution to the systems of equations given above,

\newline

a.

(6,-6)

,

\newline

b.

(3,0)

,

\newline

c.

(0,2)

,

\newline

d.

(-4,1)

Isolate $k$ in second equation: First, let's isolate $k$ in the second equation. $3 + \frac{5}{3} k = -\frac{7}{6}j$ Multiply both sides by $\frac{3}{5}$ to get $k$ alone. $k = \left(-\frac{7}{6}j\right) \cdot \left(\frac{3}{5}\right)$ $k = -\frac{7}{10}j$
Substitute $k$ into first equation: Now, substitute $k = -\frac{7}{10}j$ into the first equation. $\newline$ $-24 - 8j = 12k$ $\newline$ $-24 - 8j = 12(-\frac{7}{10}j)$
Simplify the equation: Simplify the equation. $\newline$ $-24 - 8j = -\frac{84}{10}j$ $\newline$ Multiply both sides by $10$ to clear the fraction. $\newline$ $-240 - 80j = -84j$
Add $j$ terms: Add $80j$ to both sides to get all $j$ terms on one side. $\newline$ $-240 = -4j$
Solve for j: Divide both sides by $-4$ to solve for j. $\newline$ $j = \frac{-240}{-4}$ $\newline$ $j = 60$

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