Solve each system using elimination
3x+3y=27
x-3y=-11
thx
To solve the system of equations using elimination, we can eliminate one variable by multiplying the entire equation by a suitable value to make the coefficients of one variable the same in both equations.
Let's start by eliminating the variable "y":
Multiply the second equation by 3:
3(x - 3y) = 3(-11)
3x - 9y = -33
Now, we can add the two equations together to eliminate the "y" variable:
(3x + 3y) + (3x - 9y) = 27 + (-33)
This simplifies to:
6x - 6y = -6
Now, we can divide the entire equation by 6 to solve for "x":
(6x - 6y)/6 = -6/6
x - y = -1
Now that we have an equation with only one variable, we can solve for "x". In this case, let's solve for "y" using the first equation:
3x + 3y = 27
Rearrange this equation to solve for "y":
3y = 27 - 3x
y = (27 - 3x)/3
y = 9 - x
Now that we have the value of "y", we can substitute it back into the equation we obtained earlier:
x - y = -1
x - (9 - x) = -1
Simplify the equation:
x - 9 + x = -1
2x - 9 = -1
Add 9 to both sides:
2x = 8
Divide both sides by 2:
x = 4
Now that we have the value of "x", we can substitute it back into one of the original equations to find the value of "y". Let's use the first equation:
3x + 3y = 27
Substitute x = 4:
3(4) + 3y = 27
Simplify the equation:
12 + 3y = 27
3y = 27 - 12
3y = 15
Divide both sides by 3:
y = 5
Therefore, the solution to the system of equations is x = 4 and y = 5.
To solve the system of equations using elimination, we need to eliminate one variable by adding or subtracting the equations. In this case, we can eliminate the variable "y" by adding the two equations together.
Let's start by multiplying the second equation by 3 to make the "y" terms cancel out:
3 * (x - 3y) = 3 * (-11)
3x - 9y = -33
Now we can add this equation to the first equation:
3x + 3y = 27
+ 3x - 9y = -33
___________________
6x = -6
Now we have a new equation with only one variable, "x". To solve for "x", we can divide both sides of the equation by 6:
6x = -6
x = -6/6
x = -1
Now that we have the value of "x", we can substitute it back into one of the original equations to solve for "y". Let's use the first equation:
3x + 3y = 27
3(-1) + 3y = 27
-3 + 3y = 27
3y = 27 + 3
3y = 30
y = 30/3
y = 10
Therefore, the solution to the system of equations is x = -1 and y = 10.
Add the two equations and y is instantly eliminated.
4x = 16
Take it from there.