Find the common solution for each pair of linear equations.?

Question

1. y=5x+8

y=2x-1

2.y+x=2

4x+2y=8

3.y=2x+4

y=x-16

4.4y+3x=12

2x+3y=1

Answer 1

Seriously-  no excuse to ask these here.  Do your own homework.

There are multiple techniques to solve these, learn one that you are comfortable using and just do the work.

Answer 2

1st problem:

y = 5x + 8

y = 2x - 1

5x + 8 = 2x - 1

3x = - 9

x = - 3

y = 5(- 3) + 8

y = - 15 + 8

y = - 7

Answer: x = - 3, y = - 7

2nd problem:

y + x = 2

y = 2 - x

4x + 2y = 8

2y = 8 - 4x

y = 4 - 2x

2 - x = 4 - 2x

x = 2

y = 2 - 2

y = 0

Answer: x = 2, y = 0

3rd problem:

y = 2x + 4

y = x - 16

2x + 4 = x - 16

x = - 20

y = 2(- 20) + 4

y = - 40 + 4

y = - 36

Answer: x = - 20, y = - 36

4th problem:

4y + 3x = 12

4y = 12 - 3x

y = (12 - 3x)/4

2x + 3y = 1

3y = 1 - 2x

y =  (1 - 2x)/3

3(12 - 3x) = 4(1 - 2x)

36 - 9x = 4 - 8x

x = 32

y = (12 - 3[32])/4

y = (12 - 96)/4

y = - 84/4

y = - 21

Answer: x = 32, y = - 21

Answer 3

1.

-1(y=5x+8)..........(1)

y=2x-1.........(2)

add (1)+(2)

0= -3x - 9

x=-3

y=5(-3)+8= -7

complete like this..

Answer 4

These are systems of equations, you can solve them through substitution or elimination... I'll use elimination here, where you must eliminate one of the variables through combining the equations.

1.  y= 5x+8

    -(y=2x-1)

    -y=-2x+1

     y=5x+8

    now combine the two to get:

    0=3x+9                                

    

    -9=3x

     -3=x

     now put x into one of the original equations

    y=5(-3)+8

   y=-15+8

    y=-7

   2.  -2(y+x=2)

           4x+2y=8

       -2y-2x=-4

        2y+4x=8

        2x=4

        x=2

        now put x in...

        y+2=2

        y=0

3.     y=2x+4

        -(y=x-16)

        y=2x+4

        -y=-x+16

        0=x+20

        x=-20

         put x in...

        y=2(-20)+4

        y=-40+4

        y=-36

4.     For this one you must multiply both to get a variable to cancel

       2(4y+3x=12)

       -3(2x+3y=1)

       8y+6x=24

       -9y-6x=-3

       -y=21

       y=-21

       put in y now...

         4(-21)+3x=12

        

         -84+3x=12

         3x=96

         x=33

        

Answer 5

Hey, right, 4 questions are alot, if you just can't work these, then it means that you just don't know the right technique. My advice is learn their technique instead of asking for the answer.