Q1. Solve the following equations for x,y and z:
2x + y +Z+= 11
5x + 2y + 2z = 18
x + 3y + 3z = 14
Answers
Answer:
Answer:
The solution is (x, y) = (- 13, 46)
Step-by-step explanation:
Substitution Method :-
Solve one of the equations for either x = or y = .
Substitute the solution from step 1 into the other equation.
Solve this new equation.
Solve for the second variable.
Step 1: Solve one of the equations for either x = or y = .
Given equations are 3x+2y=53 and 2x+3y=47
3x+2y=53 ................................................. ( 1 )
2x+3y=47 ..................................................( 2 )
Step 1: Solve one of the equations for either x = or y = . We will solve first equation for y.
3x + 2y = 53
subtract 3x from the sides of above equation,
2y = 53 - 3x
y = \frac{53 - 3x}{2}
2
53−3x
Step 2: Substitute the solution from step 1 into the second equation.
Put value of y in equation (2),
2x + 3y = 47
2x + 3 (\frac{53 - 3x}{2}
2
53−3x
) = 47
2x + (\frac{159 - 9x}{2}
2
159−9x
) = 47
Step 3: Solve this new equation.
Multiply by 2 on both the sides in above equation,
4x + 159 - 9x = 94
159 - 5x = 94
subtract by 159 on both the sides in above equation,
159 - 5x -159 = 94 - 159
- 5x = 65
divide both the sides by -5 in above equation,
x = - 13
Step 4: Solve for the second variable
Put x = - 13 in y = \frac{53 - 3x}{2}
2
53−3x
y\,=\,\frac{53 + 39}{2}y=
2
53+39
y\,=\,\frac{92}{2}y=
2
92
y\,=\,46y=46
The solution is: (x, y) = (- 13, 46)