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Which ordered pair is a solution of the equation?

7x-5=4y-6
Choose 1 answer:
(A) Only 
(2,4)
(B) Only 
(3,6)
(c) Both 
(2,4) and 
(3,6)
(D) Neither

Which ordered pair is a solution of the equation? \newline7x5=4y67x-5=4y-6 \newlineChoose 11 answer: \newline(A) Only (2,4)(2,4) \newline(B) Only (3,6)(3,6) \newline(C) Both (2,4)(2,4) and (3,6)(3,6) \newline(D) Neither

Full solution

Q. Which ordered pair is a solution of the equation? \newline7x5=4y67x-5=4y-6 \newlineChoose 11 answer: \newline(A) Only (2,4)(2,4) \newline(B) Only (3,6)(3,6) \newline(C) Both (2,4)(2,4) and (3,6)(3,6) \newline(D) Neither
  1. Rewrite equation in slope-intercept form: Rewrite the equation in slope-intercept form y=mx+by = mx + b.\newlineTo do this, we need to solve for yy.\newlineStart with the given equation: 7x5=4y67x - 5 = 4y - 6\newlineAdd 66 to both sides: 7x5+6=4y6+67x - 5 + 6 = 4y - 6 + 6\newlineSimplify: 7x+1=4y7x + 1 = 4y\newlineDivide both sides by 44: 7x+14=y\frac{7x + 1}{4} = y\newlineThe equation in slope-intercept form is y=74x+14y = \frac{7}{4}x + \frac{1}{4}
  2. Check ordered pair (2,4)(2, 4): Check if the ordered pair (2,4)(2, 4) satisfies the equation y=74x+14y = \frac{7}{4}x + \frac{1}{4}.\newlineSubstitute x=2x = 2 and y=4y = 4 into the equation: 4=742+144 = \frac{7}{4}\cdot 2 + \frac{1}{4}\newlineCalculate the right side: 4=72+144 = \frac{7}{2} + \frac{1}{4}\newlineFind a common denominator and add: 4=144+144 = \frac{14}{4} + \frac{1}{4}\newlineCombine the fractions: 4=1544 = \frac{15}{4}\newlineSince 44 does not equal (2,4)(2, 4)00, the ordered pair (2,4)(2, 4) is not a solution.
  3. Check ordered pair (3,6)(3, 6): Check if the ordered pair (3,6)(3, 6) satisfies the equation y=74x+14y = \frac{7}{4}x + \frac{1}{4}.\newlineSubstitute x=3x = 3 and y=6y = 6 into the equation: 6=743+146 = \frac{7}{4} \cdot 3 + \frac{1}{4}\newlineCalculate the right side: 6=214+146 = \frac{21}{4} + \frac{1}{4}\newlineCombine the fractions: 6=2246 = \frac{22}{4}\newlineSimplify the fraction: 6=5.56 = 5.5\newlineSince 66 does not equal (3,6)(3, 6)00, the ordered pair (3,6)(3, 6) is not a solution.

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