Question

Galena is solving the following system. 3x+2y+3z =5 7x+y +7z=-1 4x-4y-z=-3
Step 1 she multiplies equation (3) by 3 and adds it to equation (1)
Step 2 She multiplies equation (3) by -7 and adds it to equation (2)
which statement explains Galena’s mistake?
1 she adds equation 1 instead of equation 2 in step 1
2 She does not multiply equation 3 in step 1 by the correct value
3 She did not multiply equation 3 in step 2 by the correct value
4 she added equation 2 instead of equation 1 in step 2

Answer 1

Answer:

She did not multiply equation 3 in step 2 by the correct value.

Step-by-step explanation:

Given:

$3x+2y+3z=5\\7x+y+7z=-1\\4x-4y-z=-3$

In order to solve this, we need to eliminate any one variable and then form a simultaneous equation with the remaining two variables. Then, we nee to solve the simultaneous equation.

Here, Galena is trying to eliminate the variable $z$ first.

Step 1:  She multiplies equation (3) by 3 and adds it to equation (1)

Let us multiply equation (3) by 3

$(4x-4y-z=-3)\times 3 = (3\times 4x)-(3\times 4y)-(3\times z)=3\times -3\\(4x-4y-z=-3)\times 3 =12x-12y-3z=-9$

Now, adding this to equation 1 will cancel out z terms.

$12x-12y-3z+3x+2y+3z=-9+5\\(12x+3x)+(-12y+2y)+(3z-3z)=-4\\15x-10y+0=-4$

Now, she need to make one more equation in $x\ and \ y$.

Step 2: She multiplies equation (3) by -7 and adds it to equation (2)

Multiplying equation (3) by -7 will give,

$(4x-4y-z=-3)\times -7 = (-7\times 4x)-(-7\times 4y)-(-7\times z)=-7\times -3\\(4x-4y-z=-3)\times 3 =-28x+28y+7z=21$

Now, adding this to equation 2 will not cancel out z terms.

$-28x+28y+7z+7x+y+7z=21-1\\(-28x+7x)+(28y+y)+(7z+7z)=20\\-21x+29y+14z=20$

So, she makes mistake in step 2 as the $z$ terms are not being cancelled.

Answer 2

Answer:

She did not multiply equation 3 in step 2 by the correct value.

Step-by-step explanation: