solve equations by elimination
2x-6y=3 (1)
4x+9y=-1 (2)
Multiply first equation with -2
- 4 x + 12 y = -6
Note that, if you add down, the y's will cancel out.
- 4 x + 12 y = - 6
4 x + 9 y = - 1
( - 4 x + 4 x ) + ( 12 y + 9 y ) = -6 + ( -1 )
0 + 21 y = -6 - 1
21 y = - 7 Diwide both sides with 21
y = - 7 / 21
( Remark: 7 / 21 = 1 / 3 )
y= - 1 / 3
First equation:
2 x - 6 y = 3
2 x - 6 * ( - 1 / 3 ) = 3
2 x + 6 / 3 = 3
2 x + 2 = 3
2 x = 3 - 2
2 x = 1 Divide both sides with 2
x = 1 / 2
x = 1 / 2 , y= - 1 / 3
Thank You
To solve the given system of equations by elimination method, we need to eliminate one of the variables (x or y) by adding or subtracting the equations.
Let's start by eliminating the variable "x". We can do this by multiplying equation (1) by 2 and equation (2) by -1, so that the coefficients of "x" in both equations will be equal and opposite.
Multiplying equation (1) by 2:
2(2x - 6y) = 2(3)
4x - 12y = 6 (3)
Multiplying equation (2) by -1:
-1(4x + 9y) = -1(-1)
-4x - 9y = 1 (4)
Now, add equations (3) and (4) together to eliminate the variable "x":
(4x - 12y) + (-4x - 9y) = 6 + 1
This simplifies to:
-21y = 7
Next, divide both sides of the equation by -21 to solve for "y":
-21y / -21 = 7 / -21
y = -1/3
Now that we have the value of "y", we can substitute it back into either of the original equations to find the value of "x". Let's substitute it into equation (1):
2x - 6(-1/3) = 3
Simplifying this equation:
2x + 2 = 3
2x = 3 - 2
2x = 1
x = 1/2
So the solution to the given system of equations is:
x = 1/2
y = -1/3