What is the linear system?
2x+2y=16
4x-6y=2
I am using elimination to solve
Please help!
A linear system is a collection of equations of multiple (at least 2) unknowns similar to the equations you have shown. Each term contains a maximum of one unknown to the first degree.
Read up
http://en.wikipedia.org/wiki/Simultaneous_equations
for more information, and also the method of elimination.
If you could post your attempt at the solution, I will be pleased to look over the solution with you.
thank you, but I already know how to solve it, the problem I am having is with this certain problem because the y values are not the same, I am not sure what to do because of this
Thanks, it's much easier when you pin-point the problem!
In general, the coefficients of x and y are not the same between the two equations.
When you want to eliminate y, and the coefficients are not the same, you find the LCM (lowest common multiple) of the two coefficients and multiply each equation by the LCM/divided by the coefficient, then both coefficients will end up being the LCM.
Fist, you check if there are common factors in each equation. If there are, divide the whole equation by the common factor to reduce the equations to the lowest terms. It is not necessary, but will make your life easier.
2x+2y=16 => x+y=8
4x-6y=2 => 2x-3y=1
The LCM between the coefficients of y (1 and -3) being 3, the second equation will not change. We multiply the first equation by 3 to get
3x+3y=24
2x-3y=1
Can you take it from her now?
The linear system represents two equations in variables x and y. To solve this system using the elimination method, we need to eliminate one of the variables to find the value of the other variable.
To do this, we can multiply the first equation by -2 and the second equation by 1 to make the coefficients of x in both equations the same. This will allow us to eliminate x when we add the two equations together.
Multiply the first equation by -2:
-2(2x + 2y) = -2(16)
-4x - 4y = -32
Multiply the second equation by 1:
1(4x - 6y) = 1(2)
4x - 6y = 2
Adding the two equations together, we get:
(-4x - 4y) + (4x - 6y) = -32 + 2
-4x + 4x - 4y - 6y = -30
-10y = -30
Now that we have a new equation with just one variable, we can solve it for y by dividing both sides of the equation by -10:
-10y / -10 = -30 / -10
y = 3
Now, substitute the value of y back into one of the original equations to find x. Let's use the first equation:
2x + 2(3) = 16
2x + 6 = 16
2x = 16 - 6
2x = 10
Divide both sides of the equation by 2 to solve for x:
2x / 2 = 10 / 2
x = 5
So, the solution to the linear system is x = 5 and y = 3.
To summarize, to solve the linear system using the elimination method:
1. Multiply one or both equations by appropriate constants to make the coefficients of one variable the same in both equations.
2. Add or subtract the two equations to eliminate one variable and solve for the other variable.
3. Substitute the value of the solved variable back into one of the original equations to find the value of the other variable.
4. Verify the solution by substituting x and y back into both original equations to ensure they satisfy both equations.