2x+y=-2 (1)
x+y-z=-4 (2)
3x+5y+z=0 (3)
solve the system
need help quick!
add the last two:
4x + 6y = -4
from the 1st: y = -2-2x
sub into above new equation:
4x + 6(-2-2x) = -4
4x - 12 - 12x = -4
-8x = 8
x = -1
then y = -2+2 = 0
in the 2nd:
x+y-z=-4
-1+0-z=-4
-z=-3
z=3
x=-1
y=0
z=3
12x+4y+2z=-7 (1)
3x-12y+6z=-4 (2)
9x-16y+4z=-3 (3)
solve the system
just need the steps how to do it
To solve this system of equations, we can use the method of substitution or elimination. Let's start with the method of substitution.
Step 1: Solve Equation (1) for y:
From Equation (1), we have:
2x + y = -2
Rearranging the equation, we get:
y = -2 - 2x
Step 2: Substitute the expression for y in Equations (2) and (3):
Substituting y in Equation (2), we get:
x + (-2 - 2x) - z = -4
Simplifying:
x - 2 - 2x - z = -4
-x - z = 2
Substituting y in Equation (3), we get:
3x + 5(-2 - 2x) + z = 0
Simplifying:
3x - 10 - 10x + z = 0
-7x + z = 10
Step 3: Solve the system formed by the equations -x - z = 2 and -7x + z = 10:
We can solve this system of equations by adding the two equations together. Adding -x - z = 2 and -7x + z = 10, we get:
-8x = 12
Dividing both sides by -8, we find:
x = -3/2
Step 4: Substitute the value of x into one of the original equations to find y:
Let's use Equation (1):
2(-3/2) + y = -2
-3 + y = -2
y = -2 + 3
y = 1
Step 5: Substitute the values of x and y back into one of the original equations to find z:
Using Equation (2):
(-3/2) + 1 - z = -4
-1/2 - z = -4
-z = -4 + 1/2
-z = -7/2
z = 7/2
Therefore, the solution to the system of equations is:
x = -3/2
y = 1
z = 7/2