Btw this is algebra 2

1) what is the solution for the system of equations?

-2x+y=2 and y=4x-1

a (3/2, 5)

b (5, 3/2)

c (-2, 3/2)

d (-2, 3)

2) solve the system of equations.

x-y+z=6 and 4y+1=z and 3y=2z

a (29/5, 2/5, 3/5)

b (29/5, -2/5, -3/5)

c (31/5, -2/5, -3/5)

d (19/4, 5/2, 15/4)

3) what is the solution for the system of equations?

-4x+y=-2 and y+5=-6x

a (6/5, -16/5)

b (3/10, 16/5)

c (-3/10, -16/5)

d (-6/5, -16/5)

-2x+y=2...(i)

y=4x-1...(ii)

substitute y in (i)

-2x+(4x-1)=2

-2x+4x-1=2

-2x+4x=2+1

2x=3

2x/2=3/2

x=3/2

replacing x in (ii)

y=4(3/2)-1

y=6-1

y=5

solution=(3/2,5)

x-y+z=6 ...(i)

4y+1=z ...(ii)

3y=2z...(iii)

from(ii),

z=4y+1

substitute z in (iii)

3y=2(4y+1)

3y=8y+2

3y-8y=2

-5y=2

-5y/5=2/5

y=-2/5

substitute y in (ii)

z=4(-2/5)+1

z=-3/5

substitute z and y in (i)

x-y+z=6

x=6+y-z

x=6+(-2/5)-(-3/5)

x=31/5

solution=(31/5,-2/5,-3/5)

-4x+y=-2 ...(i)

y+5=-6x...(ii)

from (i),

y=-2+4x

substitute y in (ii)

(-2+4x)+5=-6x

-2+4x+5=-6x

-2+5=-6x-4x

3=-10x

3/-10=-10x/-10

x=-3/10

substitute x in;;y=-2+4x

y=-2+4(-3/10)

y=-2-6/5

y=-16/5

solution=(-3/10,-16/5)