9a-2b=-8 - 7a+3b=12 system of equations by elimination

So,

9a - 2b = - 8

-7a + 3b = 12

Elimination by Addition

Multiply both sides of the first equation by 3

27a - 6b = - 24

Multiply both sides of the second equation by 2

-14a + 6b = 24

Add the two equations together

13a = 0

Divide both sides by 13

a = 0

Substitute 0 for a in the first equation

9 (0) - 2b = - 8

0 - 2b = - 8

-2b = - 8

Divide both sides by - 2

b = 4

Check

9 (0) - 2 (4) = - 8

0 - 8 = - 8

-8 = - 8 This checks.

-7 (0) + 3 (4) = 12

0 + 12 = 12

12 = 12 This also checks.

S = { (0,4) }

9a - 2b = - 8

-7a + 3b = 12

Multiply the first equation by 3:

9a - 2b = - 8

27a - 6b = - 24

Multiply the 2nd equation by 2:

-7a + 3b = 12

-14a + 6b = 24

Add the two equations:

27a - 6b = - 24

-14a + 6b = 24

13a + 0 = 0

13a = 0

Divide 13 to both sides:

a = 0

Plug this into any of the two equations to find 'b':

9a - 2b = - 8

9 (0) - 2b = - 8

-2b = - 8

Divide - 2 to both sides:

b = 4

So the solution is (0, 4).