Solving for systems of equation using the elimiation method.
3x-2y=x-6
3(x+2y)=3
3x - 2y = x - 6
3(x + 2y) = 3
Lets rearrange the second equation
3(x + 2y) = 3
x + 2y = 1
Now you have:
3x - 2y = x - 6
x + 2y = 1
You want to eliminate one variable and the easiest one to do so is y. So add the two equations together like so..
3x - 2y + x + 2y = x - 6 + 1
Simplify..
4x = x - 5
3x = -5
x = -5/3
Plug back into one of the original equation and solve for y..
3(-5/3) - 2y = -5/3 - 6
-5 - 2y = -5/3 - 6
2y = 5/3 + 1
y = 4/3
So x is -5/3 and y is 4/3.
thank you for your response.
I should have included the answers the book gives.
It gives X=-7 Y=4
That's not possible. x and y are the same for both those equations. Although x = -7 and y = 4 does satisfy the second equation it does not for the first one.
3x - 2y = x - 6
3(-7) - 2(4) = -7 - 6
-21 - 8 = -7 - 6
-29 = -13 ??? This is not possible so those two values cannot be x and y. Are you sure you typed the equations right? A way for the x = -7 and y = 4 to be true is if the first equation is 3x + 2y = x - 6. So it may be a typo by the book *shrug*.
To solve a system of equations using the elimination method, you need to eliminate one of the variables by adding or subtracting the equations. Here's how you can solve this system of equations step by step:
1. Start with the given system of equations:
3x - 2y = x - 6 -- (Equation 1)
3(x + 2y) = 3 -- (Equation 2)
2. We can simplify Equation 2 by applying the distributive property:
3x + 6y = 3 -- (Equation 2 simplified)
Now we have the two equations in a suitable form for elimination.
3. The goal is to get the coefficients of one of the variables to be the same (or opposite) so that they cancel out when added or subtracted. Let's eliminate the x variable.
4. Multiply Equation 1 by 3 to make the coefficients of x the same:
3(3x - 2y) = 3(x - 6)
9x - 6y = 3x - 18 -- (Equation 1 multiplied by 3)
5. Now we can subtract Equation 1 multiplied by 3 from Equation 2:
(9x - 6y) - (3x - 18) = 3x + 6y - 3x
9x - 6y - 3x + 18 = 0
Simplify the equation:
6x - 6y + 18 = 0
6. Let's rearrange this equation:
6x - 6y = -18
7. Divide the entire equation by 6 to simplify it further:
x - y = -3
Now we have eliminated the x variable.
8. To solve for one variable, substitute the value of that variable back into one of the original equations. Let's use Equation 1:
3x - 2y = x - 6
Substitute the simplified expression for x:
3(-3) - 2y = -3 - 6
-9 - 2y = -9
9. Solve for y by isolating the variable:
-2y = -9 + 9
-2y = 0
Divide both sides by -2:
y = 0
10. Now that we have the value of y, substitute it back into one of the original equations to solve for x. Let's use Equation 1:
3x - 2y = x - 6
Substitute y = 0:
3x - 2(0) = x - 6
3x = x - 6
Combine like terms:
3x - x = -6
2x = -6
Divide both sides by 2:
x = -3
11. The solution to the system of equations is x = -3 and y = 0.