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GaryK [48]
3 years ago
13

Solve the system by substitution. *

Mathematics
1 answer:
baherus [9]3 years ago
6 0

Answer:

(-3,-1)

Step-by-step explanation:

Given equations are :

3x - 2y=-7\ ....(1)\\\\y=-7x - 22...(2)

Put the value of y from equation (2) to equation (1), so,

3x - 2(-7x - 22)=-7\\\\3x+14x+44=-7        

Taking variables on one side and constant on another side.    

17x=-7-44\\\\17x=-51\\\\x=-3

Put x = -3 in equation (2) i.e.

y=-7(-3) - 22\\\\y=-1

So, the value of x and y are (-3) and (-1) respectively.

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Galena is solving the following system. 3x+2y+3z =5 7x+y +7z=-1 4x-4y-z=-3
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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

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

Multiplying equation (3) by -7 will give,

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