Can you please help me with this one!! Solve by elimination, 3x+6y=6, 2x-3y=9
3x+6y=6
2x-3y=9
3x + 6y = 6
2(2x -3y =9)
3x + 6y = 6
4x -6y = 18
7x = 24
x = 24/7
y =-30/7
Sugma balls
Of course! To solve the system of equations using the elimination method, we will eliminate one variable by adding or subtracting the two equations. Let's start with the given equations:
Equation 1: 3x + 6y = 6
Equation 2: 2x - 3y = 9
The goal is to eliminate one variable, either x or y, by manipulating the equations so that when they are added or subtracted, one variable will be eliminated. Let's eliminate the x variable in this case:
To eliminate the x variable, we need to multiply one equation by a suitable coefficient so that the coefficients of x in both equations become opposites (one positive and one negative). In this case, let's multiply the entire Equation 1 by 2 and multiply the entire Equation 2 by 3:
Multiply Equation 1 by 2:
2(3x + 6y) = 2(6)
6x + 12y = 12
Multiply Equation 2 by 3:
3(2x - 3y) = 3(9)
6x - 9y = 27
Now, we have:
Equation 1 (after multiplication): 6x + 12y = 12
Equation 2 (after multiplication): 6x - 9y = 27
Now, we can subtract these two equations to eliminate the x variable:
(6x + 12y) - (6x - 9y) = 12 - 27
Simplifying this expression gives:
6x - 6x + 12y + 9y = 12 - 27
21y = -15
To find the value of y, divide both sides of the equation by 21:
y = -15 / 21
y = -5/7
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use Equation 1:
3x + 6y = 6
3x + 6(-5/7) = 6
3x - 30/7 = 6
To simplify further, we can multiply both sides of the equation by the reciprocal of the coefficient of x, which is 3/1:
(3/1)(3x - 30/7) = (3/1)(6)
9x - 90/7 = 18/1
Simplifying further, we have:
9x - 90/7 = 18
9x = 18 + 90/7
To simplify the right side of the equation, we need a common denominator:
9x = (18*7 + 90) / 7
9x = (126 + 90) / 7
9x = 216 / 7
Finally, we can divide both sides of the equation by 9 to solve for x:
x = (216 / 7) / 9
x = 216 / (7*9)
x = 216 / 63
x = 24/7
Therefore, the solution to the system of equations 3x + 6y = 6 and 2x - 3y = 9 is x = 24/7 and y = -5/7.