the first equation of the system is muti plied by 2. by what number would you mutiply the second equation to elimi nate the x variable by adding? first: 6x - 5y equals 21 second: 4x plus 7y equals 15 and another one is the first equation of the system is muti plied by 4. by what number would you mutiply the second equation to elimi nate the y variable by adding? first: 2x plus 5y equals 16 second: 8x 4y equals 10
See my comments to kyle, who is probably someone you know
Show your work in algebraic form and help will be provided
To eliminate the x variable by adding, you need to determine the number by which you should multiply the second equation so that when you add the two equations together, the x terms cancel out.
For the first set of equations:
Equation 1: 6x - 5y = 21
Equation 2: 4x + 7y = 15
Since the first equation is multiplied by 2, to eliminate the x variable, you would need to multiply the second equation by -3. This can be found by taking the coefficient of x in the first equation (-6) and dividing it by the coefficient of x in the second equation (4), resulting in -6/4 = -3.
After multiplying the second equation by -3, you get:
-3(4x + 7y) = -3(15)
-12x - 21y = -45
Now you can add the two equations together:
(6x - 5y) + (-12x - 21y) = 21 + (-45)
-6x - 26y = -24
The x variable has been eliminated.
For the second set of equations:
Equation 1: 2x + 5y = 16
Equation 2: 8x - 4y = 10
Since the first equation is multiplied by 4, to eliminate the y variable, you would need to multiply the second equation by 5. This can be found by taking the coefficient of y in the first equation (5) and dividing it by the coefficient of y in the second equation (-4), resulting in 5/(-4) = -5/4.
After multiplying the second equation by 5, you get:
5(8x - 4y) = 5(10)
40x - 20y = 50
Now you can add the two equations together:
(2x + 5y) + (40x - 20y) = 16 + 50
42x - 15y = 66
The y variable has been eliminated.