Question

Solve the system of linear equations below, using substitution method.

8x+9y=368x+9y=36
3x+4y=163x+4y=16

Answer 1

Given:

The system of equations is

`8x+9y=36`

`3x+4y=16`

To find:

The solution of the given system of equations using the substituting method.

Solution:

We have,

`8x+9y=36` ...(i)

`3x+4y=16` ...(ii)

From (ii), we get

`3x=16-4y`

`x=(16-4y)/(3)` ...(iii)

Putting this value in (i), we get

`8\left((16-4y)/(3)\right)+9y=36`

Multiply both sides by 3.

`8(16-4y)+27y=108`

`128-32y+27y=108`

`-5y=108-128`

`y=(-20)/(-5)`

`y=4`

Putting y=4 in (iii), we get

`x=(16-4(4))/(3)`

`x=(16-16)/(3)`

`x=(0)/(3)`

`x=0`

Therefore, the solution of given system of equations is (0,0).