Multiple choice

Solve graphically the pair of equations $x+3y=6$, and $3x-5y=18$. Hence, find the value of $K$ if $7x+3y=K$

  1. $x=-3, y=1, K=13$
  2. $x=-8, y=5, K=8$
  3. $x=1, y=2, K=29$
  4. $x=6, y=0, K=42$
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D Correct answer
Explanation

Solving the system x+3y=6 and 3x-5y=18: multiply the first by 3 to get 3x+9y=18. Subtracting the second from this gives 14y=0, so y=0 and x=6. Substituting into 7x+3y=K gives 7(6)+3(0)=42.

AI explanation

Multiplying the first equation by 3 gives 3x + 9y = 18. Subtracting the second equation from this result eliminates x and leaves 14y = 0, so y = 0. Substituting y = 0 into x + 3y = 6 gives x = 6. Finally, substituting these values into 7x + 3y = K results in K = 42.

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