Could someone give me an example of a linear eqution using elimination to solve the systems of equations?
Thanks!!!
What I don't get is that in my book the question is {2x - 3= - 5y and -2y = -3y + 1}. How do I put the question in standard form?
A little help, please!!! :-)
Just move all the x's and y's to one side, and the numbers to the other side:
2x - 3 = -5y
-2x = -3y + 1
becomes
2x + 5y = 3
-2x + 3y = 1
add them together to eliminate the x's
0x + 8y = 4
y = 1/2
so,
x = 1/4
If I misread -2y = -3y + 1 then you can surely fix it and get the expected answer.
In most cases it is best to have the x's and y's on one side, with the constant on the other side
2x - 3 = -5y becomes
2x + 5y = 3
Your other equation probably has a typo, I was expecting an x term instead there are two y terms.
Anyway, get the x's and y's to the left, and the constant to the right.
Then proceed in the way that Steve illustrated above.
Sure! Let's consider the following system of equations:
Equation 1: 2x + 3y = 8
Equation 2: 4x - y = 10
To solve this system of equations using the elimination method, we'll eliminate one variable by adding or subtracting the equations.
In this case, let's eliminate the "y" variable.
Step 1: Multiply Equation 2 by 3 to make the coefficients of "y" match with Equation 1.
Equation 1: 2x + 3y = 8
Equation 2: 12x - 3y = 30
Step 2: Add Equation 1 with Equation 2 to eliminate the "y" variable.
(2x + 3y) + (12x - 3y) = 8 + 30
14x = 38
Step 3: Solve for "x" by dividing both sides of the equation by 14.
14x/14 = 38/14
x = 19/7
Now that we have found the value of "x," we can substitute it back into either Equation 1 or Equation 2 to find the value of "y."
Let's substitute it into Equation 1:
2(19/7) + 3y = 8
38/7 + 3y = 8
3y = 8 - 38/7
Now solve for "y":
3y = (56 - 38)/7
3y = 18/7
y = 6/7
Therefore, the solution to the system of equations is x = 19/7 and y = 6/7.
2x + 7y = 16
x - 3y = -5
multiply the 2nd equation by 2
2x + 7y = 16
2x - 6y = -10
subtract the equations to eliminate x:
0x + 13y = 26
y = 2
so,
x = 1