i just don't get this elimination method ..... plz help me plz.....teach me how to keep the x and y in a parallel line. and which number to multiply.....plz help
-5x-4y=-11
10x=-6-y
help me plz......
Pick any number that will multiply by one of the equations to give the same number as in the other equation. For example, if we multiply equation 1 by 2 we would have
-10x-8y=-22. Why did I pick 2 as a multiplier. Because it gives me -10x and 10x agrees with the x in equation 2 (the sign is different but that's ok). Then adding equation 1 to equation 2 will eliminate x because -10x+10x = 0x. OK?
-5x-4y=-11
10x=-6-y
line them up - something*x + something*y = something
-5 x - 4 y = -11
10 x + 1 y = -6
we could now multiply the first equation by 2 to make the absolute value of the x coefficient 10 for both -then eliminate x by adding them
or
we could multiply the second by 4 to make the absolute value of the y coefficient 4 for both. then eliminate y by subracting them.
Lets do the second and eliminate y:
-5 x - 4 y = -11
40 x + 4 y = -24
------------------ now add
+35 x +0 y = -35
so
x = 35/35 = -1 now go back and use either equation to find y
y = -10(-1) -6
y = 4
oo......thanks to both of you so much
iwnt help wth reduction formulas
-5x - 4y = -11
10x = -6 - y
For the second equation, move -y to the left side and change sign to positive.
-5x - 4y = -11
10x + y = -6
Now you are either going to eliminate the x's or y's first.
If it is x's, then multiply the first equation by 2.
If it is y's, then multiply the second equation by 4.
I'll PICK THE SECOND EQUATION
4(10x + y) = 4(-6)
40x + 4y = -24
-5x - 4y = -11
40x + 4y = -24
_______________________
35x = -35 > divide by 35 on both sides
x = -1
Now solve for y by plugging in x value in either equation.
-5(-1) -4y = -11
5 - 4y = -11
-5 -5
______________________
-4y = -16 > divide by -4 on both sides.
y = 4
Take any three lines K,M and P.Draw as many lines as you can by joining them in pairs..what is the maximum number of different lines as you can draw?
Sure, I can help you understand the elimination method for solving a system of equations. In the elimination method, we aim to eliminate one variable by adding or subtracting the equations. Let's work on the given equations:
-5x - 4y = -11 ...(1)
10x = -6 - y ...(2)
To keep the x and y terms in a parallel line, we need to make sure the coefficients (the numbers multiplying x and y) have opposite signs in both equations.
In equation (2), let's rearrange it to match the format of equation (1):
y = -6 - 10x
Now, we can see that the coefficient of y in equation (1) is -4, while in equation (2) it is -1. To make the coefficients the same, we need to multiply equation (2) by 4. Multiplying an entire equation by a number does not change the equation's solution.
4 * (10x) = 4 * (-6 - y)
40x = -24 - 4y
Now, our equations look like this:
-5x - 4y = -11 ...(1)
40x = -24 - 4y ...(3)
The coefficients of y in both equations are -4, which makes them parallel.
Next, we can add equation (1) and equation (3) together to eliminate the y-term:
(-5x - 4y) + (40x) = (-11) + (-24 - 4y)
Simplifying:
-5x - 4y + 40x = -11 - 24 - 4y
35x - 4y = -35
Now, we have a new equation:
35x - 4y = -35
By eliminating the y-term, we are left with a single equation involving only x. To solve for x, we can isolate it by moving the -4y term to the other side by adding 4y to both sides:
35x = 4y - 35
Finally, we need to solve for y. To do that, we substitute the value of 35x from equation (4) into equation (1):
-5x - 4y = -11
Replace 35x with 4y - 35:
-5(4y - 35) - 4y = -11
Simplify and solve for y:
-20y + 175 - 4y = -11
-24y + 175 = -11
-24y = -186
y = -186 / -24
y = 7.75
Now that we know the value of y, we can substitute it back into equation (2) to solve for x:
10x = -6 - y
Substitute y = 7.75:
10x = -6 - 7.75
10x = -13.75
x = -13.75 / 10
x = -1.375
Therefore, the solution to the system of equations is x = -1.375 and y = 7.75.