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Determine whether or not the ordered pair is a solution to the equation

y=3x+8
(a) 
(-5,-7)
(b) 
(-1,3)
(c) 
((1)/(3),g)

Determine whether or not the ordered pair is a solution to the equation\newliney=3x+8 y=3 x+8 \newline(a) (5,7) (-5,-7) \newline(b) (1,3) (-1,3) \newline(c) (13,g) \left(\frac{1}{3}, g\right)

Full solution

Q. Determine whether or not the ordered pair is a solution to the equation\newliney=3x+8 y=3 x+8 \newline(a) (5,7) (-5,-7) \newline(b) (1,3) (-1,3) \newline(c) (13,g) \left(\frac{1}{3}, g\right)
  1. Given Equation: We are given the equation y=3x+8y=3x+8 and we need to check if the ordered pairs (5,7)(-5,-7), (1,3)(-1,3), and (13,g)(\frac{1}{3},g) are solutions to this equation. We will substitute the xx-value from each ordered pair into the equation and check if the corresponding yy-value satisfies the equation.
  2. Ordered Pair (5,7)(-5,-7): For the ordered pair (5,7)(-5,-7), substitute x=5x = -5 into the equation y=3x+8y=3x+8. \newliney=3(5)+8y = 3*(-5) + 8 \newliney=15+8y = -15 + 8 \newliney=7y = -7 \newlineCheck if this is equal to the yy-value from the ordered pair. \newline7=7-7 = -7 \newlineSince the values match, (5,7)(-5,-7) is a solution to the equation.
  3. Ordered Pair (1,3)(-1,3): For the ordered pair (1,3)(-1,3), substitute x=1x = -1 into the equation y=3x+8y=3x+8.\newliney=3(1)+8y = 3*(-1) + 8\newliney=3+8y = -3 + 8\newliney=5y = 5\newlineCheck if this is equal to the yy-value from the ordered pair.\newline535 \neq 3\newlineSince the values do not match, (1,3)(-1,3) is not a solution to the equation.
  4. Ordered Pair (13,g)\left(\frac{1}{3},g\right): For the ordered pair (13,g)\left(\frac{1}{3},g\right), substitute x=13x = \frac{1}{3} into the equation y=3x+8y=3x+8. \newliney=3(13)+8y = 3\left(\frac{1}{3}\right) + 8 \newliney=1+8y = 1 + 8 \newliney=9y = 9 \newlineCheck if this is equal to the yy-value from the ordered pair. \newlineSince we do not have a specific value for gg, we cannot determine if (13,g)\left(\frac{1}{3},g\right) is a solution unless (13,g)\left(\frac{1}{3},g\right)00.

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