Elimination
X+2y=5
-3x+6y=15
Multiply top equation by 3 and then add the equations.
3x + 6y = 15
-3x + 6y = 15
12y = 30
You can take it from this point.
To solve this system of equations by elimination, we need to eliminate one variable so that we can solve for the other.
Let's start by multiplying the first equation by 3:
3(X+2y) = 3(5)
3X + 6y = 15
Now, we have two equations:
3X + 6y = 15 ...(1)
-3x + 6y = 15 ...(2)
Notice that the second equation has the same coefficient for the y variable, but with opposite signs. To eliminate the y variable, we can subtract equation (2) from equation (1) by subtracting corresponding terms:
(3X + 6y) - (-3x + 6y) = 15 - 15
3X + 6y + 3x - 6y = 0
(3X + 3x) + (6y - 6y) = 0
3X + 3x = 0
3(X+x) = 0
Now, we have:
3(X+x) = 0
Dividing both sides of the equation by 3, we get:
X + x = 0
This simplifies to:
2X = 0
Dividing both sides of the equation by 2, we get:
X = 0
Now that we have the value of X, we can substitute it back into one of the original equations to solve for y.
Using the first equation:
X + 2y = 5
Substituting X = 0:
0 + 2y = 5
2y = 5
Dividing both sides of the equation by 2, we get:
y = 5/2
Therefore, the solution to the system of equations is X = 0 and y = 5/2.