2x + y = -5
3x +5y = 3
How come I have to multiply by 5 to make the y variables cancel, like what does that mean? I don't get how ur supposed to multiply like where and how? Im really stuck right now, please help:(
2x + y = -5
3x +5y = 3
to solve 2 equations simultaneously (at the same time), by elimination, the object is to get rid of one variable.
adding a negative to a positive equals zero, for example, 5y + -5y = 0.
So, to get rid of y in the above 1st equation, since the first equation has just "y" and the second equation has "5y", you multiply the first equation by -5 to get "-5y" so that the -5y added to 5y = 0,
Multiply the whole equation by -5
-5 (2x + y = -5) = -10x - 5y = 25
Now add the two equations together
-10x - 5y = 25
3x + 5y = 3
-7x + 0 = 28
-7x = 28
x = -4
substitute x = -4 in either equation and solve for your y value
do you understand this?
Wow helper:D
Thanks a lot buddy, I really appreciate all the time you put to help me with my question. Yeah thanks to your explanation I get it, thanks a lot:)
So here's how I substitute right?
2x+y = -5
2(-4)+y = -5
-8 +y = -5
Then I add 8 to both sides and get:
y = -3
Therefore the solution would be:
(-4,3)
correct, the answer is (-4, 3)
When solving a system of linear equations like the one you provided, one common method is to use elimination to cancel out one of the variables. In this case, it seems like you want to cancel out the y variable.
To do that, you can multiply the first equation by a number that will cause the coefficient of y in the first equation to be the same as the coefficient of y in the second equation. This ensures that when you add or subtract the two equations, the y terms will cancel out.
In the original equations:
2x + y = -5 --> Equation 1
3x + 5y = 3 --> Equation 2
Let's focus on canceling the y terms. The coefficients of y in Equation 1 and Equation 2 are 1 and 5, respectively. Multiplying Equation 1 by 5 will give us the same coefficient of y in both equations.
Multiply Equation 1 by 5:
5 * (2x + y) = 5 * (-5)
10x + 5y = -25 --> Equation 3
Now we have:
10x + 5y = -25 --> Equation 3
3x + 5y = 3 --> Equation 2
By multiplying Equation 1 by 5, we now have two equations with the same coefficient (5) for the y term. At this point, you can either subtract Equation 2 from Equation 3 or subtract Equation 3 from Equation 2 to eliminate the y variable.
For example, let's subtract Equation 2 from Equation 3:
(10x + 5y) - (3x + 5y) = (-25) - (3)
10x + 5y - 3x - 5y = -25 - 3
7x = -28
Now we have a new equation:
7x = -28
To solve for x, we can divide both sides of the equation by 7:
7x/7 = -28/7
x = -4
Now that we found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use Equation 1:
2x + y = -5
2(-4) + y = -5
-8 + y = -5
y = -5 + 8
y = 3
Therefore, the solution to the system of equations is x = -4 and y = 3.
Remember, the process of multiplying by a number to cancel out variables is just one method. There are other methods to solve systems of equations, such as substitution or using matrices.