System of Equations?

Question

This has been bothering me for quite a while now ever since I realized I forget it but how do you solve for system of equations? 
a) 
y = 5x − 2 

y = 2x + 10 
~~~~~~~~~~~~~~~~~~~~ 
b) 
x = −2y − 1 

2x + y = −20

Answer 1

(a)

y = 5x − 2   --------(1) 

y = 2x + 10   --------(2)

Subtract equation (2) from (1) .

0 = 3x - 12 ⇒ 3x = 12 ⇒ x = 4

Now Substitute x = 4 in the equation (1) .

y = 5(4) − 2 ⇒20 -2 ⇒ 18

So x = 4 and y = 18 .

Answer 2

(b)

x = −2y − 1  -----------(1)

2x + y = −20

Rewrite the above equation .

x = -y/2 -10  -------------(2)

Subtract equation (2) from (1) .

0 = -3y/2 + 9 ⇒ 3y = 18

                      ⇒ y = 6

Now Substitute y = 6 in the equation (1) .

x = −2(6) − 1 ⇒ -12 -1 = -13

So x = -13 and y = 6 .