4y-x=27 2x+7y=21

Question

Use the substitution method to solve this system.

Answer 1

Multiply this equation by 2 : [4y-x=27] x 2

we are multiplying by 2 so that -2x and +2x cancel each other out and we can solve for one of the unknowns y. The trick here is to somehow solve for one unknown first

8y-2x = 54

Now, rearrange and solve for unknowns

-2x +8y = 54

2x   +7y =21

Adding, we get,

15 y = 75

or y= 5

Note: -2x and + 2x cancel each other out.

Now, plug y  =5  in one of the equations to get x

4 y - x = 27

4 (5 )- x = 27

x = -7

 

Answer 2

The first equation:

4y - x = 27;

4y - 27 = x.

Second equation:

2 (4y - 27) + 7y = 21;

8y - 54 + 7y = 21;

15y = 75;

y = 5.

x = 4(5) - 7 = -7.

The answer is thus (-7, 5).

Answer 3

y = 5, x = -7.

Solve your first equation for x: x = 4y - 27. Then substitute x in the second equation by this expression. It gives you:

                      2(4y - 27) +7y = 21   or 15y - 54 = 21

Solve it for y: y= 75/15 = 5. Put it back into the first equation to find x = - 7.