Solve the system of equations by the addition method.?

Question

Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.

x + 3y = 6
9x + 4y = 8
(-2, 0)
(1, 1)
No solution, inconsistent
(0, 2)

Answer 1

You already got the answer.
x = 0, y = 2
This works in both equations. It's not inconsistent.

Answer 2

x + 3y = 6
9x + 4y = 8

multiply 1st equation by -9 on both side
-9(x + 3y) = -9(6)
-9x - 27y = -54
add to 2nd equation

-9x - 27y = -54
+9x + 4y = + 8

0x - 23y = -46
y = 2 solve for x in any equation

x + 3(2) = 6
x = 0

Sooo (0 , 2)

Answer 3

x + 3y = 6 multiply both sides by -9
-9x-27y=-54
9x + 4y = 8 add to equation above
-23y=-46 divide both sides by -23
y=2
x+3y=6 substitute 2 for y
x+2*3=6
x+6=6 subtract 6 from each side
x=0
(0, 2) is the answer

Answer 4

Multiply first equation by -4 -12x +16y = -4 then ADD THE TWO EQUATIONS 12x - y = -11 15y = -15 divide both sides by 15 y = -1 substitute -1 for y to solve for x 3x - 4(-1) = 1 3x +4 = 1 subtract 4 from both sides 3x = -3 divide both sides by 3 x = -1 (-1, -1)

Answer 5

Multiply the first equation by 9 and subtract the equations.
9x+27y=54
9x+4y=8
23y=46
y=2
x+3(2)=6
x=0
Ans (0,2)

Answer 6

multiply the first equation by -9, then add to the second;

-9x -27y = -54
9x + 4y = 8
---------------------
0 - 23y = -46

y = 2

x + 3(2) = 6
x + 6 = 6

x = 0

Answer 7

***- 9x - 27y = - 54
*****9x + 4y = 8-----ADD

- 23y = - 46
y = 2

x + 6 = 6
x = 0

Solution is (0 , 2)