Sole the following system of equation by elimination
3x+2y=24
2x+3y=26
Yes.
Well, I could solve the system of equations for you, but I'm more inclined to make you laugh instead! So, let's see if I can come up with a funny response that might bring a smile to your face.
Why did the system of equations go to therapy?
Because it couldn't solve its own problems!
To solve the system of equations by elimination, we need to eliminate one variable by adding or subtracting the equations. Here are the steps:
Step 1: Multiply both sides of the first equation by 2, and multiply both sides of the second equation by 3 to make the coefficients of x in both equations the same.
2(3x+2y) = 2(24)
3(2x+3y) = 3(26)
Simplifying these equations gives us:
6x + 4y = 48
6x + 9y = 78
Step 2: Now, subtract the equations from each other in order to eliminate the x variable:
(6x + 9y) - (6x + 4y) = 78 - 48
Simplifying this equation gives us:
5y = 30
Step 3: Solve for y by dividing both sides of the equation by 5:
5y/5 = 30/5
y = 6
Step 4: Substitute the value of y (y = 6) back into one of the original equations (either the first or the second) to solve for x. Let's use the first equation:
3x + 2(6) = 24
Simplifying the equation gives us:
3x + 12 = 24
Step 5: Now, isolate x by subtracting 12 from both sides of the equation:
3x + 12 - 12 = 24 - 12
3x = 12
Step 6: Solve for x by dividing both sides of the equation by 3:
3x/3 = 12/3
x = 4
So, the solution to the system of equations is x = 4 and y = 6.
To solve the system of equations by elimination, we need to eliminate one variable by adding or subtracting the equations. Let's start by eliminating the variable "x":
1. Multiply the first equation by 2:
2(3x + 2y) = 2(24)
6x + 4y = 48
2. Multiply the second equation by 3:
3(2x + 3y) = 3(26)
6x + 9y = 78
Now we have two equations with the same coefficient for "x" (6x), but with opposite signs. By subtracting the equations, the "x" term will be eliminated:
(6x + 9y) - (6x + 4y) = 78 - 48
6x - 6x + 9y - 4y = 30
5y = 30
Now we can solve for "y" by dividing both sides of the equation by 5:
5y/5 = 30/5
y = 6
We have found the value of "y" as 6. To find the value of "x", we substitute this value back into one of the original equations. Let's use the first equation:
3x + 2(6) = 24
3x + 12 = 24
3x = 24 - 12
3x = 12
x = 12/3
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 6.
You want to eliminate 1variable.
Multiply the 1st equation by 3
9x + 6y = 72
Multiply the 2nd equation by -2
-4x - 6y +-52
Combine the two equations to get 5x =20 or x = 4
Replace x with 4 in either of the original equations to find y.
Then you should check in both equations.