Help Solving Systems of Equations in 3 Variables

Hi All,

My issue is solving 3 systems of variables that are missing a variable in each equation.

My 3 systems are:

3p + 2r = 11, (1)

q - 7r = 4, (2)

p - q = 1 (3)

What I'm seeing is - that there's no q in equation (1). That means that q has been eliminated from one equation. Since I need another equation with q eliminated, I wanted to use equations (2) and (3) to eliminate q.

With that said, I proceeded with:

Multiplied equation (2) by 1 and added it to equation (3)

q - 7r = 4

p - q =1

----------

p - 7r = 5 (4)

Next, I multiplied equation (4) by - 3 and added it to equation (1)

3p + 2r = 11

-3p + 21r = -15

----------------

23r = -4

r = -4/23 (fraction)

Whenever, I get fraction that confuses me as to how to solve for the other variables. I plugged -4/23 back into equation (1) to solve for p and got an improper fraction. Is this correct? Or, can someone provide some assistance with how I should've proceeded in the first place? I'm missing something here and I'm not sure how I should proceed? Please help. TIA...

help me trying to so problem for a variable

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for the variable x

for the variable w

for the variable y

for the variable z

plz need help trying to cheach up in class so i can pass any one is welcome

Quote:

Originally Posted by

**lilrhino** Hi All,

My issue is solving 3 systems of variables that are missing a variable in each equation.

My 3 systems are:

3p + 2r = 11, (1)

q - 7r = 4, (2)

p - q = 1 (3)

What I'm seeing is - that there's no q in equation (1). That means that q has been eliminated from one equation. Since I need another equation with q eliminated, I wanted to use equations (2) and (3) to eliminate q.

With that said, I proceeded with:

Multiplied equation (2) by 1 and added it to equation (3)

q - 7r = 4

p - q =1

----------

p - 7r = 5 (4)

Next, I multiplied equation (4) by - 3 and added it to equation (1)

3p + 2r = 11

-3p + 21r = -15

----------------

23r = -4

r = -4/23 (fraction)

Whenever, I get fraction that confuses me as to how to solve for the other variables. I plugged -4/23 back into equation (1) to solve for p and got an improper fraction. Is this correct? Or, can someone provide some assistance with how I should've proceeded in the first place? I'm missing something here and I'm not sure how I should proceed? Please help. TIA...