Question

What is the answer to the system of equations problem
3x=2y+10
9y=3x-7

Answer 1

Solving:


`\left \{ {{3x = 2y + 10} \atop {9y = 3x-7}} \right.`
Organize by putting the unknowns left and right the numbers without letter, changing the signal when changing sides.

`\left \{ {{3x-2y=10\:(I)} \atop {-3x+9y=-7\:(II)}} \right.`
Eliminate opposites (+ 3x and -3x)

`\left \{ {{\diagup\!\!\!\!3x-2y=10} \atop {-\diagup\!\!\!\!3x+9y=-7}} \right.`

`\left \{ {{-2y=10} \atop {9y=-7}} \right.`
----------------------------

`7y = 3`

`\boxed{y = (3)/(7) }`

Now substitute the found value "y" in the first equation:

`3x-2y=10\:(I)`

`3x-2* (3)/(7) =10`

`3x- (6)/(7) = 10`

`(21x)/(\diagup\!\!\!\!7) - (6)/(\diagup\!\!\!\!7) = (70)/(\diagup\!\!\!\!7)`

`21x - 6 = 70`

`21x = 70 + 6`

`21x = 76`

`\boxed{x = (76)/(21) }`

Answer:

`(x,y) = ( (76)/(21) , (3)/(7) )\end{array}}\qquad\quad\checkmark`



Taking the truth proof


`3x - 2y = 10\:(I)`

`3* (76)/(21) - 2* (3)/(7) = 10`

`(228)/(21) - (6)/(7) = 10`

`(1596-126)/(147) = 10`

`(1470)/(147) = 10`

`10 = 10\:(TRUE)`