Solve the system of linear equations by using substitution m

Solve the system of linear equations by using substitution method. 4x + 3y = 11 x - 3y = -1 5. Solve the system of linear equations by using substitution or elimination method. X - y - z = 0 2x + 3y - 6z = 2 3x + 2y = 16

Solution

4x + 3y = 11

x-3y = -1

Substitution

x = 3y-1

substitute x = 3y-1 into eq 1.

4(3y-1)+3y = 11

12y-4+3y = 11

15y-4 = 11

15y = 11+4

15y = 15

dividing by 15 on both sides

y = 1

x = 3y-1 so x = 3-1 = 2

so x = 2, y = 1

2) x-y-z = 0

2x-3y+6z = 2

3x+2y = 16

Let us eliminate z

x-y- z = 0 => x-y = z

2x-3y+6(x-y) = 2

8x-9y = 2

3x+2y = 16

to eliminate multiply 8 with 3 and 3 with 8.

24x-27y = 6

24x+16y = 128

subtracting above equations.

43y = 122

1: Multiply first equation by 2 and add the result to the second equation. The result is:

x-y-z = 0

5y-4z = 2

3x+2y = 16

Step 2: Multiply first equation by 3 and add the result to the third equation. The result is:

  

x-y-z = 0

5y-4z = 2

5y+3y = 16

Step 3: Multiply second equation by 1 and add the result to the third equation. The result is:

  

x-y-z = 0

5y-4z = 2

7z = 14

Step 4: solve for z.

z = 2

Step 5: solve for y.

5y-4z=2 => 5y-8 = 2 => y =2

Step 6: solve for x by substituting y=2 and z=2 into the first equation.

x = 4

so x = 4 y = 2, y = 2