5x+3y-5z=542x-3y+2z=-74x-2y+4z=-2ne ed the three solution set

5x+3y-5z=54 ...(1)

2x-3y+2z=-7 ...(2)

4x-2y+4z=-2 ...(3)

Let's add equation (1) and (2) to eliminate y.

So, (5x+2x)+(3y-3y)+(-5z+2z)=54-7

7x-3z=47 ...(4)

Now we need to make the equal coefficient of y's of equation (2) and (3) to eliminate y by using these two equations.

So, multiply equation (2) by 2 and (3) by -3. Therefore,

2*(2x-3y+2z=-7) 4x-6y+4z=-14

-3*(4x-2y+4z=-2) -12x+6y-12z=6

-8x-8z=-8 (By adding two equations).

x+z=1 (Divided each sides by -8). ...(5)

3x+3z=3 (Multiply each sides by 3)

Now add this equation with equation (4)

3x+3z=3

7x-3z=47

10x=50

So, x=5 (Divided each sides by 10).

Now plug in x=5 in equation (5). So,

5+z=1

z=1-5

z=-4

Now plug in the values of x and z in equation (1) to get the value of y. So,

5(5)+3y-5(-4)=54

25+3y+20=54

3y+45=54

3y=54-45

3y=9

y=3.

So, the solution set is x=5, y=3 and z=-4.

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