To solve this system of equations, we can use the method of substitution or elimination.
Given equations:1) 2x + y = 912) x + 2y = 623) y - 2z = 9
First, let's solve equations 1 and 2 using the method of elimination:Multiply equation 2 by 2:4) 2(x + 2y) = 2(62)2x + 4y = 124
Subtract equation 1 from equation 4 to eliminate x:2x + 4y - 2x - y = 124 - 913y = 33y = 33 / 3y = 11
Now, substitute y = 11 into equation 1 to solve for x:2x + 11 = 912x = 91 - 112x = 80x = 80 / 2x = 40
Now that we have found x = 40 and y = 11, we can substitute them into equation 3 to solve for z:11 - 2z = 9-2z = 9 - 11-2z = -2z = -2 / -2z = 1
Therefore, x = 40, y = 11, and z = 1.
To solve this system of equations, we can use the method of substitution or elimination.
Given equations:
1) 2x + y = 91
2) x + 2y = 62
3) y - 2z = 9
First, let's solve equations 1 and 2 using the method of elimination:
Multiply equation 2 by 2:
4) 2(x + 2y) = 2(62)
2x + 4y = 124
Subtract equation 1 from equation 4 to eliminate x:
2x + 4y - 2x - y = 124 - 91
3y = 33
y = 33 / 3
y = 11
Now, substitute y = 11 into equation 1 to solve for x:
2x + 11 = 91
2x = 91 - 11
2x = 80
x = 80 / 2
x = 40
Now that we have found x = 40 and y = 11, we can substitute them into equation 3 to solve for z:
11 - 2z = 9
-2z = 9 - 11
-2z = -2
z = -2 / -2
z = 1
Therefore, x = 40, y = 11, and z = 1.