Question

Solve using substitution
3x - 9y = 3
6x - 3y = -24

Solve using elimination
y - 1/2x = 6
2x + 6y = 19

Answer 1

3x - 9y = 3
6x - 3y = -24

from the first, divide by 3
x - 3y = 1
x = 3y+1

sub into the 2nd
6(3y+1) - 3y = -24
18y + 6 - 3y = -24
15y = -30
y = -2
then x = -6+1 = -5

for the 2nd system, multiply the 1st by -4
2x -4y = -24
2x + 6y = 19
subtract them
10y = 43
y = 43/10 = 4.3
into the 2nd:
2x + 6(4.3) = 19
2x = 19 - 25.8
2x = -6.8
x = -3.4

Answer 2

Eq1: 3x - 9y = 3
Eq2: 6x - 3y = -24

In Eq1, solve for X:
3x = 9y + 3
X = 3y+1

In Eq2, replace X with 3y+1:
6(3y+1) - 3y = -24
18y+6 - 3y = -24
15y = -30
Y = -2.

In Eq1, replace Y with-2:
3x-9*(-2) = 3
3x + 18 = 3
3x = -15
X = -5.

Solution set: (-5,-2).

Eq1: Y - X/2 = 6
Eq2: 2x + 6y = 19

Multiply Eq1 by 4 and add Eq2:
-2x + 4y = 24
+2x + 6y = 19
Sum: 10y = 43
Y = 4.3

In Eq1, replace Y with 4.3:

4.3 - 0.5x = 6
-0.5x = 1.7
X = -3.4

Solution set: (-3.4,4.3).

Answer 3

Reiny, we meet again!! LOL! Oh well, we
got the same answer!