Consider the equations 3x+2=14 and 2+3x=14 Do they have the same solution? Why or why not?

1 answer:

7 0

Yes, on the left side you are adding 3x+2 in one and 2+3x in the other. these add to the same number because addition is Commutative on the real numbers.

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A line passes trough the point { 0, -3/2} and has a slope of 1/2. what is the equation of the line?

Luden [163]

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6 0

3 years ago

6x + 4y=10 12x + y= -29

Olin [163]

Answer: x=-3 y=7.

Step-by-step explanation:

$\displaystyle\\\left \{ {{6x+4y=10\ \ \ \ \ (1)} \atop {12x+y=-29\ \ \ \ (2)}} \right.\\ We\ multiply\ both\ sides\ of\ equation\ (1)\ by\ -2:\\\left \{ {{(-2)*6x+(-2)*4y=(-2)*10} \atop {12x+y=-29}} \right. \\\\\left \{ {{-12x-8y=-20} \atop {12x+y=-29}} \right. \\$ $We\ summarize\ equations\ (1)\ and\ (2):\\-7y=-49\\-7*y=-7*7\\Divide\ both\ sides\ of\ the\ equation\ by\ -7:\\y=7.\\We\ substitute\ the\ value\ of\ y\ into \ equation\ (1):\\6x+4*7=10\\6x+28=10\\6x+28-28=10-28\\6x=-18\\6*x=6*(-3)\\Divide\ both\ sides\ of\ the\ equation\ by\ 6:\\x=-3.$