Question

Solve the equations (the answer might be no solution or all real numbers)4(A + 4) - 9(A - 4)= 3711=7 - (1- y)3+7(p - 10)= - 38 -(5 -3p)20 + 5(3-5A)= -5(A-6)+5

Answer 1

Consider the following equations:

Equation 1:

`4\mleft(A+4\mright)-9\mleft(A-4\mright)=37`

Equation 2:

`11=7-1-y`

Equation 3:

`3+7\mleft(p-10\mright)=-38-\mleft(5-3p\mright)`

Equation 4:

`20+5\mleft(3-5A\mright)=-5\mleft(A-6\mright)+5`

From equation 1, we get:

`4A\text{ + 16-9A+36= 37}`

this is equivalent to:

`4A\text{ -9A = 37-16-36}`

this is equivalent to:

`-5A\text{ = -15}`

solving for A, we get:

`A\text{ = }(15)/(5)=\text{ 3}`

then A = 3.

From equation 4, we get:

`20\text{ + 15 -25A = -5A +30+5}`

this is equivalent to:

`-25A+5A\text{ = 30 +5 -20-15}`

this is equivalent to:

`-20A\text{ = }0`

Thus A = 0.

But this is a contradiction since we had found that A =3. Then, the linear system has no solution (is incongruent).