Solve the system by the elimination method.

2a + 3b = 6

5a + 2b - 4 = 0

Make in form

ax+by=c

add 4 to both sides in 2nd equaiton

5a+2b=4

now

elimiate a variable

I choose b

multiply top equation by - 2 and 2nd by 3

add

-4a-6b=-12

15a+6b=12 +

11a+0b=0

11a=0

a=0

nice

sub back

5a+2b=4

5 (0) + 2b=4

2b=4

divide 2

b=2

a=0

b=2

if in form (a, b)

(0,2)

2a + 3b = 6 - - > Equation 1

5a + 2b = 4 - - > Equation 2

Equation 1 * 5 - - > 10a + 15b = 30

Equation 2 * 2 - - > 10a + 4b = 8

Equation 1 - Equation 2 - - > 11b = 22 - - > b = 2

Sub b=2 in Equation 1 (or 2, either works):

2a + 3b = 6

2a + 3 (2) = 6

2a + 6 = 6

2a = 0

a = 0

b = 2, a = 0