Question

Solve the system by the elimination method.

2a + 3b = 6
5a + 2b - 4 = 0

Answer 1

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)

Answer 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