A "solution" is a pair of numbers ... one for 'x' and one for 'y' ... that make the equation
a true statement when you put them in place of 'x' and 'y'.
There are an infinite number of them.
the simplest form of 5x + 3y +2x - 6y is 7x-3y
To determine the number of possible solutions for the equations (x - 3y = -3) and (-2x + 6y = 12), we can first rewrite the second equation. Notice that (-2x + 6y = 12) can be simplified to (x - 3y = -6) by dividing everything by -2. The first equation and the simplified second equation represent parallel lines since they have the same slope but different y-intercepts, meaning they do not intersect. Thus, there are no solutions to these equations.
x - 3y = -3: multiply by -2 giving -2x + 6y = 6, but -2x + 6y = 12 so we have a problem! Misprint?
2x - 3y = 62x = 3y + 63y = 2x - 6y = (2x - 6)/3y = (2/3)x - 2
5x + 6y + 3y - 2x you have to add like terms. add the y terms and then the x terms 9y + 3x this is your answer
6x + 3y + 6y - 2x = (6x - 2x) + (3y + 6y) = 4x + 9y
the simplest form of 5x + 3y +2x - 6y is 7x-3y
To determine the number of possible solutions for the equations (x - 3y = -3) and (-2x + 6y = 12), we can first rewrite the second equation. Notice that (-2x + 6y = 12) can be simplified to (x - 3y = -6) by dividing everything by -2. The first equation and the simplified second equation represent parallel lines since they have the same slope but different y-intercepts, meaning they do not intersect. Thus, there are no solutions to these equations.
Collect like terms: 2x + 3y + 3y - 5 - 6 2x + 6y - 11
5x -6y=-30 5x-6y=30 (2x+3y) (2x-3y)=30 4x+6y=30 4x=30 x=30/4
x - 3y = -3: multiply by -2 giving -2x + 6y = 6, but -2x + 6y = 12 so we have a problem! Misprint?
2x - 3y = 62x = 3y + 63y = 2x - 6y = (2x - 6)/3y = (2/3)x - 2
The equations are identical in value, ie the second is merely twice the first...
5x + 6y + 3y - 2x you have to add like terms. add the y terms and then the x terms 9y + 3x this is your answer
It is: 2(x+3y) when factored
Let's see. 2X + 3Y = 12 3Y = - 2X + 12 Y = -2/3X + 4 ---------------- 6Y - 4X = 2 6Y = 4X + 2 Y = 2/3X + 1/3 --------------------- Nope. They can't be. Plot a few points and see.
20x2 + 22xy + 6y2 = 20x2 + 10xy + 12xy + 6y2 = 10x(2x + y) + 6y(2x + y) = (2x + y)(10x + 6y) = 2(2x + y)(5x + 3y)