Solve the system.
2x+9y=4
6y-2z=1
-4x+4z=0
same way as the one below
right off x = z
https://www.jiskha.com/display.cgi?id=1506187203
To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the method of substitution.
Step 1: Solve equation 1 for x:
Rearrange the equation 1 to solve for x:
2x + 9y = 4
2x = 4 - 9y
x = (4 - 9y) / 2
Step 2: Substitute the expression for x in equations 2 and 3:
Substitute x into equation 2:
6y - 2z = 1
Substitute x into equation 3:
-4(4 - 9y) / 2 + 4z = 0
Step 3: Simplify equation 3:
Multiply -4 by each term within the parentheses:
-16 + 36y / 2 + 4z = 0
-8 + 18y + 4z = 0
18y + 4z = 8
Step 4: Solve equation 2 for z:
Rearrange equation 2 to solve for z:
6y - 2z = 1
-2z = 1 - 6y
z = (6y - 1) / 2
Step 5: Substitute the expression for z into equation 4:
18y + 4((6y - 1) / 2) = 8
18y + 2(6y - 1) = 8
18y + 12y - 2 = 8
30y - 2 = 8
30y = 10
y = 10 / 30
y = 1/3
Step 6: Substitute the value of y into equations 1 and 2 to find x and z:
Substitute y = 1/3 into equation 1:
x = (4 - 9(1/3)) / 2
x = (4 - 3)/2
x = 1/2
Substitute y = 1/3 into equation 2:
z = (6(1/3) - 1) / 2
z = (2 - 1) / 2
z = 1/2
Therefore, the solution to the system of equations is:
x = 1/2, y = 1/3, and z = 1/2.