So I've been working on solving this system by addition/subtraction and I just can't get the right answer. Her is the system of equations I was given to solve by add/sub:
3x – y = –12
x + 2y = –18
double the first:
6x - 2y = -24
x + 2y = -18
add them:
7x = -42
x = -6
back into the second:
-6 + 2y = -18
2y = -12
y = -6
x = -6 , y = -6
solve the system by substitution
6x+2y=-18
-x+5y=19
To solve this system of equations using addition or subtraction (also known as the method of elimination), we want to eliminate one variable by adding or subtracting the equations. The goal is to create a new equation in which one variable is eliminated, allowing us to solve for the remaining variable.
In this case, let's eliminate the variable "y" by adding the two equations:
Starting with:
3x – y = –12
x + 2y = –18
To eliminate "y," we need the coefficients in front of "y" to be the same or opposite. In this case, the coefficients are -1 and 2, which are already opposite. To make them equal, we can multiply the first equation by 2:
2(3x – y) = 2(-12)
6x - 2y = -24
Now, we have:
6x - 2y = -24
x + 2y = –18
Adding these two equations eliminates "y" because the -2y and 2y cancel each other out:
(6x + x) + (-2y + 2y) = -24 + (-18)
7x + 0 = -42
7x = -42
Now, we can solve for "x" by dividing both sides of the equation by 7:
7x / 7 = -42 / 7
x = -6
We have found the value of "x" to be -6. To find the value of "y," we can substitute this value back into either of the original equations. Let's use the first equation:
3x – y = –12
3(-6) – y = –12
-18 - y = -12
-y = -12 + 18
-y = 6
Finally, let's solve for "y" by multiplying both sides of the equation by -1 to eliminate the negative sign:
(-1)(-y) = (-1)(6)
y = -6
Therefore, the solution to the given system of equations is x = -6 and y = -6.