44(j+2k)=12 22 k=-11 j+16 Consider the system of equations. How many solutions (j,k) does this system have? Choose 1 answer: (A) 0 (B) Exactly 1 (c) Exactly 2 (D) Infinitely many

Simplify the first equation: Simplify the first equation. The first equation is 44(j+2k)=12. To simplify, divide both sides by 44 to isolate (j+2k). j + 2k = 12 / 44 j + 2k = 3 / 11Simplify the second equation: Simplify the second equation. The second equation is 22k = -11j + 16. To simplify, divide both sides by 22 to isolate k. k = (-11j + 16) / 22 k = -1/2 j + 8/11Compare the two simplified equations: Compare the two simplified equations. We have j + 2k = 3/11 and k = -1/2 j + 8/11. We can substitute the expression for k from the second equation into the first equation to solve for j. j + 2(-1/2 j + 8/11) = 3/11Solve for j: Solve for j. Distribute the 2 in the first equation: j - j + 16/11 = 3/11 Notice that j - j cancels out, leaving us with: 16/11 = 3/11Check for consistency: Check for consistency. We see that 16/11 does not equal 3/11. This means that there is no value of j that can satisfy both equations simultaneously.Determine the number of solutions: Determine the number of solutions. Since there is no value of j that can satisfy both equations, there is no solution to the system of equations.

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44(j+2k)=12

22 k=-11 j+16
Consider the system of equations. How many solutions
(j,k) does this system have?
Choose 1 answer:
(A) 0
(B) Exactly 1
(c) Exactly 2
(D) Infinitely many

$44(j+2 k)=12$ $\newline$ $22 k=-11 j+16$ $\newline$ Consider the system of equations. How many solutions $(j, k)$ does this system have? $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) Exactly $1$ $\newline$ (C) Exactly $2$ $\newline$ (D) Infinitely many

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Math Problems

Algebra 1

Find the number of solutions to a system of equations

Full solution

44(j+2 k)=12

\newline

22 k=-11 j+16

\newline

Consider the system of equations. How many solutions

(j, k)

does this system have?

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B) Exactly

1

\newline

2

\newline

(D) Infinitely many

Simplify the first equation: Simplify the first equation. $\newline$ The first equation is $44(j+2k)=12$ . To simplify, divide both sides by $44$ to isolate $(j+2k)$ . $\newline$ $j + 2k = \frac{12}{44}$ $\newline$ $j + 2k = \frac{3}{11}$
Simplify the second equation: Simplify the second equation. $\newline$ The second equation is $22k = -11j + 16$ . To simplify, divide both sides by $22$ to isolate $k$ . $\newline$ $k = \frac{-11j + 16}{22}$ $\newline$ $k = -\frac{1}{2} j + \frac{8}{11}$
Compare the two simplified equations: Compare the two simplified equations. $\newline$ We have $j + 2k = \frac{3}{11}$ and $k = -\frac{1}{2} j + \frac{8}{11}$ . We can substitute the expression for $k$ from the second equation into the first equation to solve for $j$ . $\newline$ $j + 2\left(-\frac{1}{2} j + \frac{8}{11}\right) = \frac{3}{11}$
Solve for j: Solve for j. $\newline$ Distribute the $2$ in the first equation: $\newline$ $j - j + \frac{16}{11} = \frac{3}{11}$ $\newline$ Notice that $j - j$ cancels out, leaving us with: $\newline$ $\frac{16}{11} = \frac{3}{11}$
Check for consistency: Check for consistency. $\newline$ We see that $\frac{16}{11}$ does not equal $\frac{3}{11}$ . This means that there is no value of $j$ that can satisfy both equations simultaneously.
Determine the number of solutions: Determine the number of solutions. $\newline$ Since there is no value of $j$ that can satisfy both equations, there is no solution to the system of equations.