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Chapter 3: Q7. (page 142)

Solve each system of equations.

2r+3s-4t=204r-s+5t=133r+2s+4t=15

Short Answer

Expert verified

The solution isr=5,s=-2,t=-1.

Step by step solution

01

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

Given system of equations are

2r+3s-4t=204r-s+5t=133r+2s+4t=15

Multiplying second equation by 3 and adding to the first equation, we get

2r+12r-4t+15t=20+3914r+11t=59

Again multiplying second equation by 2 and adding to the third equation, we get

8r+3r+10t+4t=26+1511r+14t=41

02

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

System of two equations with two variables are

14r+11t=5911r+14t=41

Multiplying the first equation by 11 and second by 14 and subtracting them we get

121t-196t=649-574-75t=75t=-1

Putting the value of in equation we get

14r-11=5914r=59+1114r=70r=5

03

Step-3 –Finding the value of using the value o f   r  and t

Putting the value of r and t in the equation4r-s+5t=13we get,

4(5)-s+5(-1)=1320-s-5=13-s=13-15-s=-2s=2

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