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{:[y < 3x+4],[y < 5x+2]:} Which of the following ordered pairs (x,y) satisfies the system of inequalities? Choose 1 answer: (A) (-1,0) (B) (1,7) (C) (2,11) (D) (3,-4)

ylt;3x+4ylt;5x+2 \begin{array}{l} y&lt;3 x+4 \\ y&lt;5 x+2 \end{array} \newlineWhich of the following ordered pairs (x,y) (x, y) satisfies the system of inequalities?\newlineChoose 11 answer:\newline(A) (−1,0) (-1,0) \newline(B) (1,7) (1,7) \newline(C) (2,11) (2,11) \newline(D) (3,−4) (3,-4)

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Q. y<3x+4y<5x+2 \begin{array}{l} y<3 x+4 \\ y<5 x+2 \end{array} \newlineWhich of the following ordered pairs (x,y) (x, y) satisfies the system of inequalities?\newlineChoose 11 answer:\newline(A) (−1,0) (-1,0) \newline(B) (1,7) (1,7) \newline(C) (2,11) (2,11) \newline(D) (3,−4) (3,-4)
  1. Test (−1,0)(-1,0) in 11st inequality: Test the ordered pair (−1,0)(-1,0) in the first inequality y < 3x+4. Substitute −1-1 for xx and 00 for yy. 0 < 3(-1) + 4 0 < -3 + 4 0 < 1 Since 0 < 1 is true, (−1,0)(-1,0) satisfies the first inequality.
  2. Test (−1,0)(-1,0) in 22nd inequality: Test the ordered pair (−1,0)(-1,0) in the second inequality y < 5x+2. Substitute −1-1 for xx and 00 for yy. 0 < 5(-1) + 2 0 < -5 + 2 0 < -3 Since 0 < -3 is false, (−1,0)(-1,0) does not satisfy the second inequality.
  3. Test (1,7)(1,7) in 11st inequality: Test the ordered pair (1,7)(1,7) in the first inequality y < 3x+4. Substitute 11 for xx and 77 for yy. 7 < 3(1) + 4 7 < 3 + 4 7 < 7 Since 7 < 7 is false (77 is not less than 77), (1,7)(1,7) does not satisfy the first inequality.
  4. Move to next pair: Since (1,7)(1,7) does not satisfy the first inequality, there is no need to test it in the second inequality. We can move on to the next ordered pair.
  5. Test (2,11)(2,11) in 11st inequality: Test the ordered pair (2,11)(2,11) in the first inequality y < 3x+4. Substitute 22 for xx and 1111 for yy. 11 < 3(2) + 4 11 < 6 + 4 11 < 10 Since 11 < 10 is false, (2,11)(2,11) does not satisfy the first inequality.
  6. Move to next pair: Since (2,11)(2,11) does not satisfy the first inequality, there is no need to test it in the second inequality. We can move on to the next ordered pair.
  7. Test (3,−4)(3,-4) in 11st inequality: Test the ordered pair (3,−4)(3,-4) in the first inequality y < 3x+4.\newlineSubstitute 33 for xx and −4-4 for yy.\newline-4 < 3(3) + 4\newline-4 < 9 + 4\newline-4 < 13\newlineSince -4 < 13 is true, (3,−4)(3,-4) satisfies the first inequality.
  8. Test (3,−4)(3,-4) in 22nd inequality: Test the ordered pair (3,−4)(3,-4) in the second inequality y < 5x+2. Substitute 33 for xx and −4-4 for yy. -4 < 5(3) + 2 -4 < 15 + 2 -4 < 17 Since -4 < 17 is true, (3,−4)(3,-4) satisfies the second inequality.
  9. Solution found: Since the ordered pair (3,−4)(3,-4) satisfies both inequalities, it is the solution to the system of inequalities.

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