Answer :
Doing process of elimination can take a long time, especially if you do not have answers to chose from.
I would start by getting x by itself in one of the equations. The easiest way to go about doing this is changing x - 3y = 0 to
x = 3y.
Now that we know that x equals 3y, we can replace all the x's in the other equation with 3y. This makes the equation
3y - 6 = 2(3y), now we need to combine like terms. Multiply 2 and 3y, to get 3y - 6 = 6y, and then subtract 3y from both sides to get -6 = 3y. Divide both sides by 3, and then get that -2 = y in other words y = -2. After you know what y equals, plug y into one of the equations and solve for x. I did
x - 3(-2) = 0. Multiply -3 by -2, and get x - 6 = 0. Then add six to both sides and then you get that x = 6.
Plug both values into the equation to check the answer. (:
I would start by getting x by itself in one of the equations. The easiest way to go about doing this is changing x - 3y = 0 to
x = 3y.
Now that we know that x equals 3y, we can replace all the x's in the other equation with 3y. This makes the equation
3y - 6 = 2(3y), now we need to combine like terms. Multiply 2 and 3y, to get 3y - 6 = 6y, and then subtract 3y from both sides to get -6 = 3y. Divide both sides by 3, and then get that -2 = y in other words y = -2. After you know what y equals, plug y into one of the equations and solve for x. I did
x - 3(-2) = 0. Multiply -3 by -2, and get x - 6 = 0. Then add six to both sides and then you get that x = 6.
Plug both values into the equation to check the answer. (:
Answer:
the solution of the given system of equation is {(-6,-2)}
Step-by-step explanation:
The system of equations is given by
[tex]x-3y=0...(i)\\\\3y-6=2x...(ii)[/tex]
Solve the equation (i) for x
[tex]x-3y=0\\\\x=3y[/tex]
Substitute this value of x in equation (ii) and solve for y
[tex]3y-6=2\cdot3y\\\\3y-6=6y\\\\-3y=6\\\\y=-2[/tex]
Plugging this value of y in the equation x = 3y
[tex]x=3\cdot(-2)\\\\x=-6[/tex]
Therefore, the solution of the given system of equation is {(-6,-2)}
Check the solution:
Substitute the value of x and y in original equations
For equation (i)
[tex]x-3y=0\\\\-6-3(-2)=0\\\\-6+6=0\\\\0=0[/tex]
For equation (ii)
[tex]3(-2)-6=2(-6)\\\\-6-6=-12\\\\-12=-12[/tex]
We got true results for both the equations.
Hence, the solution is correct.
Therefore, the solution of the given system of equation is {(-6,-2)}