Solve the following system of linear equations using the elimination method

x=-1, y=2, z=3

Step-by-step explanation:

First at all, you can divide these equations into two group. It is easier to you.

4x-2y+3z=1

3x+y+2z=5

x+3y-4z=-7

3x+y+2z=5

Then, you can simplify these group of equation that you divided.

So, we have to simplify these step by step.

First, we can simplify the first group of equation.

4x-2y+3z=1

3x+y+2z=5

We have to find which variable you want to eliminate. I choose y.

You can multiply the second equation of first group by 2 and eliminate them.

4x-2y+3z=1

6x+2y+4z=10

As the variable of y is same and we can eliminate y by addition.

4x-2y+3z=1

6x+2y+4z=10

become

10x+0+7z=11

10x+7z=11

10x+7z=11 as the third equation.

Next, simplify the second group of equation.

x+3y-4z=-7

3x+y+2z=5

Same way as the previous one. We need to find which variable that you want to eliminate. I choose y.

We need to balance for the first equation x+3y-4z=-7 at least one variable.

We need to multiply this equation by -3 below to get the same value of y to eliminate the above equation.

3x+y+2z=5 (multiply by -3)

-9x-3y-6z=-15

x+3y-4z= -7

-9x-3y-6z= -15

Here we go! Now these group has same value and variable to eliminate.

We can eliminate these equations by addition method.

x+3y-4z= -7

-9x-3y-6z= -15

-8x+0+10z= -22

-8x+10z= -22

Furthermore, we have to combine these equations that we have simplified from the previous groups.

10x+7z=11

-8x+10z= -22

10x+7z=11 and -8x+10z= -22 as a new group.

Finally, it is time to solve these equations!!

10x+7z=11

-8x+10z= -22

First equation of the above group, we can multiply by 10. Like this:

100x+70z=110

Second equation of the above group, we can multiply by 7. Like this:

-56x+70z=-154

So, we can see there are same value from these equation which are +70z and -70z.

Now, we can eliminate this variable by sum these equations.

100x+70z=110

-56x+70z=-154

44x= -44

x= -1

When we get x= -1 , we can use this value to any equation that you want. You can get the same answer as well.

When x= -1,

substitute into 100x+70z=110

100(-1)+70z=110

-100+70z=110

70z=110+100

70z=210

z=3

When z=3 and x= -1, we can substitute into x+3y-4z= -7

-1+3y-4(3)= -7

-1+3y-12= -7

3y=6

y=2

So, the answer is x= -1 , y=2 , z=3

I hope you will understand my solution and explanation. Bye!!

can you rephrase the question ? it is unclear : -)

step-by-step explanation: