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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+2k)=12 44(j+2 k)=12 \newline22k=−11j+16 22 k=-11 j+16 \newlineConsider the system of equations. How many solutions (j,k) (j, k) does this system have?\newlineChoose 11 answer:\newline(A) 00\newline(B) Exactly 11\newline(C) Exactly 22\newline(D) Infinitely many

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Q. 44(j+2k)=12 44(j+2 k)=12 \newline22k=−11j+16 22 k=-11 j+16 \newlineConsider the system of equations. How many solutions (j,k) (j, k) does this system have?\newlineChoose 11 answer:\newline(A) 00\newline(B) Exactly 11\newline(C) Exactly 22\newline(D) Infinitely many
  1. Simplify the first equation: Simplify the first equation.\newlineThe first equation is 44(j+2k)=1244(j+2k)=12. To simplify, divide both sides by 4444 to isolate (j+2k)(j+2k).\newlinej+2k=1244j + 2k = \frac{12}{44}\newlinej+2k=311j + 2k = \frac{3}{11}
  2. Simplify the second equation: Simplify the second equation.\newlineThe second equation is 22k=−11j+1622k = -11j + 16. To simplify, divide both sides by 2222 to isolate kk.\newlinek=−11j+1622k = \frac{-11j + 16}{22}\newlinek=−12j+811k = -\frac{1}{2} j + \frac{8}{11}
  3. Compare the two simplified equations: Compare the two simplified equations.\newlineWe have j+2k=311j + 2k = \frac{3}{11} and k=−12j+811k = -\frac{1}{2} j + \frac{8}{11}. We can substitute the expression for kk from the second equation into the first equation to solve for jj.\newlinej+2(−12j+811)=311j + 2\left(-\frac{1}{2} j + \frac{8}{11}\right) = \frac{3}{11}
  4. Solve for j: Solve for j.\newlineDistribute the 22 in the first equation:\newlinej−j+1611=311j - j + \frac{16}{11} = \frac{3}{11}\newlineNotice that j−jj - j cancels out, leaving us with:\newline1611=311\frac{16}{11} = \frac{3}{11}
  5. Check for consistency: Check for consistency.\newlineWe see that 1611\frac{16}{11} does not equal 311\frac{3}{11}. This means that there is no value of jj that can satisfy both equations simultaneously.
  6. Determine the number of solutions: Determine the number of solutions.\newlineSince there is no value of jj that can satisfy both equations, there is no solution to the system of equations.

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