Solve the system by addition 2x-4y=7,4x+2y-1 can show one show me how to do this.
First, try to see if you can cancel out any of the variables by adding the equations.
4x+2y-1 also equals 4x+2y=1
(4x+2y=1)(2) = 8x+4y=2
now, add the two equations and see the y cancel out.
2x-4y=2
8x+4y=2
10x=4
x=4/10=2/5
Plug this number back into the equation (any of those two) and find y.
i still do see how you got that answer i got 2x-4y=7 ,4x+2y=-1. 6x+6y=6 isn't that how you do it please help understand better
T.T
the purpose oft using addition here is to add them in such a way so that one of the variables will cancel out
leave the first equation alone
2x-4y=7, multiply the second by 2
8x+4y=-2, now add them
10x + 0 = 5
x = 1/2
back in the first....
2(1/2)-4y=7
1-4y=7
-4y=6
y=-3/2
You just added them to get 6x+6y=6
Even though that new equation is valid and true it gets you nowhere.
To solve the system of equations using the method of addition (also known as the method of elimination), we'll first multiply one or both equations by a constant to ensure that the coefficients of one of the variables will cancel out.
Given the system of equations:
2x - 4y = 7 (Equation 1)
4x + 2y = 1 (Equation 2)
Let's multiply Equation 1 by 2 to ensure that the coefficients of the x terms will cancel out when added to Equation 2:
2(2x - 4y) = 2(7)
4x - 8y = 14 (Equation 3)
Now, we have the system of equations:
4x - 8y = 14 (Equation 3)
4x + 2y = 1 (Equation 2)
We can now add Equation 2 and Equation 3 to eliminate the x terms.
(4x - 8y) + (4x + 2y) = 14 + 1
Simplifying the equation:
(4x + 4x) + (-8y + 2y) = 15
8x - 6y = 15 (Equation 4)
Now we have the system of equations:
8x - 6y = 15 (Equation 4)
4x + 2y = 1 (Equation 2)
Next, we can multiply Equation 2 by 2 to ensure that the coefficients of the y terms will cancel out when added to Equation 4:
2(4x + 2y) = 2(1)
8x + 4y = 2 (Equation 5)
Now we have the system of equations:
8x - 6y = 15 (Equation 4)
8x + 4y = 2 (Equation 5)
We can subtract Equation 5 from Equation 4 to eliminate the y terms:
(8x - 6y) - (8x + 4y) = 15 - 2
Simplifying the equation:
(8x - 8x) + (-6y - 4y) = 13
-10y = 13
Now, we solve for y by dividing both sides of the equation by -10:
-10y/(-10) = 13/(-10)
y = -13/10
Now that we have found the value of y, we can substitute it back into either Equation 2 or Equation 3 to solve for x. Let's use Equation 2:
4x + 2(-13/10) = 1
Simplifying the equation:
4x - 26/10 = 1
4x = 1 + 26/10
4x = (10 + 26)/10
4x = 36/10
x = 9/5
Therefore, the solution to the system of equations is x = 9/5 and y = -13/10.