use the elimination method to solve this and what integer do you multiply in the 2nd equation
1. 6x + 3y = 14
2.3x + 2y = 10
To multiply the second equation to eliminate y, you would multiply the entire equation by 3.
1. 6x + 3y = 14
2. 9x + 6y = 30
Now you can subtract the first equation from the second equation to eliminate y:
(9x + 6y) - (6x + 3y) = 30 - 14
3x = 16
x = 16/3
Now substitute x back into the first equation to solve for y:
6(16/3) + 3y = 14
32 + 3y = 14
3y = -18
y = -6
Therefore, the solution to the system of equations using the elimination method is x = 16/3 and y = -6.
so, what Integer do you multiply the 2nd equation?
Apologies for the confusion in my previous response.
To eliminate y, we need to multiply the second equation by 3.
2. 3x + 2y = 10
2 * 3: 6x + 4y = 30
Now the system of equations is:
1. 6x + 3y = 14
2. 6x + 4y = 30
Now subtract the first equation from the second equation:
(6x + 4y) - (6x + 3y) = 30 - 14
y = 16
Now substitute y back into the first equation to solve for x:
6x + 3(16) = 14
6x + 48 = 14
6x = -34
x = -34/6
x = -17/3
Therefore, the solution to the system of equations using the elimination method is x = -17/3 and y = 16. And you should multiply the 2nd equation by 3 to eliminate y. Thanks for the clarification.
3 is not a option the options are 2, 6, -2 and -1/2
Apologies for the oversight. Let's reassess the options.
Given equations:
1. 6x + 3y = 14
2. 3x + 2y = 10
To eliminate y, we need to find a factor that when multiplied by the second equation will result in equal coefficients for y in both equations.
Looking at the options, if we multiply the second equation by -2, we get:
-2(3x + 2y) = -2(10)
-6x - 4y = -20
The system of equations becomes:
1. 6x + 3y = 14
2. -6x - 4y = -20
Now, add the two equations:
6x + 3y + (-6x) + (-4y) = 14 + (-20)
-y = -6
y = 6
Substitute y back into the first equation to find x:
6x + 3(6) = 14
6x + 18 = 14
6x = -4
x = -4/6
x = -2/3
Therefore, the solution to the system of equations when the second equation is multiplied by -2 is x = -2/3 and y = 6. The correct integer to multiply the second equation is -2.