Q. Which ordered pair is a solution of the equation? 7x−5=4y−6Choose 1 answer: (A) Only (2,4)(B) Only (3,6)(C) Both (2,4) and (3,6)(D) Neither
Rewrite equation in slope-intercept form: Rewrite the equation in slope-intercept formy=mx+b.To do this, we need to solve for y.Start with the given equation: 7x−5=4y−6Add 6 to both sides: 7x−5+6=4y−6+6Simplify: 7x+1=4yDivide both sides by 4: 47x+1=yThe equation in slope-intercept form is y=47x+41
Check ordered pair (2,4): Check if the ordered pair (2,4) satisfies the equation y=47x+41.Substitute x=2 and y=4 into the equation: 4=47⋅2+41Calculate the right side: 4=27+41Find a common denominator and add: 4=414+41Combine the fractions: 4=415Since 4 does not equal (2,4)0, the ordered pair (2,4) is not a solution.
Check ordered pair (3,6): Check if the ordered pair (3,6) satisfies the equation y=47x+41.Substitute x=3 and y=6 into the equation: 6=47⋅3+41Calculate the right side: 6=421+41Combine the fractions: 6=422Simplify the fraction: 6=5.5Since 6 does not equal (3,6)0, the ordered pair (3,6) is not a solution.
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