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Chapter 3: Q14. (page 142)

Solve each system of equations.

14

5x+2y=43x+4y+2z=67x+3y+4z=29

Short Answer

Expert verified

The solution is x=2,y=-3,z=6..

Step by step solution

01

Step-1 –Using elimination to obtain two equations with two variables

Given system of equations are

5x+2y=43x+4y+2z=67x+3y+4z=29

Multiplying the second equation by 2and subtracting from the third equation, we get

7x鈭�6x+3y鈭�8y=29鈭�12x鈭�5y=17

02

Step-2 –Solving the system of two equations with two variables

5x+2y=4x鈭�5y=17System of two equations with two variables are

Multiplying the second equation by 5and subtracting from the first equation, we get

2y+25y=4鈭�8527=鈭�81y=鈭�3

Putting the value ofyin the second equation, we get

x鈭�5y=17x鈭�5(鈭�3)=17x+15=17x=17鈭�15x=2

03

Step-3 –Substituting the value ofx and y in any equation with three variables

3x+4y+2z=63(2)+4(鈭�3)+2z=66鈭�12+2z=62z=6+62z=12z=6.

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