To cancel out the x variables, we can multiply the first equation by 2 and the second equation by -3:
2(3x+4y) = 2(48)
-3(6x+2y) = -3(60)
where are you getting the numbers to cancel them out?
To cancel out the x variables in the given equations, we can choose any numbers as long as the multiplication by those numbers results in the coefficients of x being equal in magnitude but opposite in sign. In this case, we chose to multiply the first equation by 2 and the second equation by -3. These numbers were chosen arbitrarily to simplify the problem and are not necessarily the only numbers that would work to cancel out the x variables.
To cancel out the x variables, we need to find coefficients that, when multiplied with the equations, will result in the same value for x. In this case, we need to find coefficients for the equations so that the resulting coefficients for the x variable are equal but opposite in sign.
To cancel out the x variables, we can choose any coefficients as long as the resulting coefficients for x are equal and opposite. In this example, we can choose the coefficients 2 and -3. By multiplying the first equation by 2 and the second equation by -3, we ensure that the coefficients for x become -6x in both equations.
The multiplication of the equations is as follows:
2(3x + 4y) = 2(48)
-3(6x + 2y) = -3(60)
This results in the coefficients for x cancelling out and simplifying the equations. The numbers 2 and -3 are arbitrary coefficients chosen to achieve this cancellation.
To cancel out the x variables, we need to manipulate the equations in a way that when we add or subtract them, the x terms will cancel each other out. In this case, we can multiply the first equation by 2 and the second equation by -3.
To understand why we chose these specific numbers, let's go through the steps:
First, let's look at the coefficients of the x term in each equation. In the first equation, the coefficient of x is 3, and in the second equation, the coefficient of x is 6.
We can choose the numbers to multiply each equation by in a way that when we add or subtract the two equations, the x terms will cancel out. In this case, since the coefficients of x are 3 and 6, we need to find a common multiple of these two numbers. The least common multiple (LCM) of 3 and 6 is 6. Therefore, we multiply the first equation by 2 to get a coefficient of 6 for the x term (2 * 3 = 6), and we multiply the second equation by -3 to get a coefficient of -6 for the x term (-3 * 6 = -18/3 = -6).
By multiplying the first equation by 2 and the second equation by -3, we ensure that when we add/subtract the two equations, the x terms will cancel each other out because they have the same coefficient, but opposite signs.
So, multiplying the first equation by 2 gives us:
2 * (3x + 4y) = 2 * 48
6x + 8y = 96
And multiplying the second equation by -3 gives us:
-3 * (6x + 2y) = -3 * 60
-18x - 6y = -180
Now, when we add these two equations together, the x terms will cancel out:
(6x + 8y) + (-18x - 6y) = 96 + (-180)
-12x + 2y = -84
Therefore, by multiplying the first equation by 2 and the second equation by -3, we can cancel out the x variables and simplify the system of equations.