5x+2y=10....(1)

x-8y=12....(2)

Method one (substituting )

From (2) we could obtain:

x=8y+12

Now substitute in (1)

5(8y+12)+2y=10

40y+60+2y=10

42y=-50

==> y=-50/42= -25/21

==> x= 8y+12=-8(25/21)+12= -200/21+12=52/21.

Second method (adding equations):

Multiply equation (1) with 4:

==> 20x+8y=40

x-8y=12

Now add both equation:

21x= 52

==> x= 52/21

==> y= (x-12)/8= (52/21 -12)/8= -25/21

5x+2y = 10............(1)

x-8y =12...........(2)

Solution:

from the 2nd x = 12+8y. We substitute this fin eq(1). Then eq (1) becomes:

5(12+8y)+2y = 10.

60+40y+2y =10

42y = 10-60 = -50. Or

y = -50/42 = -25/21, So from the 2nd eq, x = (12+8y) = 12+8(-25/21) = 52/21

So x= 52/21 and y = -25/21

The first method is that in which a variable, from the 2, could be written depending on the other one, x or y, from the one of the equations of the system.

For example,from the second equation, we'll write

x = 12 + 8y

We'll substitute x, in the first equation, by the expression above, in this way:

5( 12 + 8y ) + 2y = 10

60 + 40y + 2y = 10

42y = - 50

**y = - 25/21**

x = 12 + 8*( -25/21 )

**x = 52/21**

The second method is to form in both equations, similar terms and combine them. For example, we want to form similar terms in y. For this reason, we'll multiply by 4, the first equation, and after that, we'll add the second equation to the first one. We'll combine the similar terms.

20x + 8y + x - 8y = 40 + 12

21x = 52

**x = 52/21**

52/21 - 8y = 12

8y = - 200/21

**y = - 25/21**