Can someone check my answers on these? Thank you!!
Solve each system using addition or subtraction.
1. x+y=8
x-y=4
For the solution I got (6,3)
2. x-3y=7
x+2y=2
For the solution I got (4,-1)
3. 5s+2t=6
9s+2t=22
For the solution I got (-4,13)
4. 2x+3y=13
x-3y=2
For the solution I got (5,1)
5. 2m-5n=-6
2m-7n=-14
I got (7,-4)
6. 3r-5s=-35
2r-5s=-30
I need help on this one!!!
1. Correct
2. Correct
3.
5 s + 2 t = 6
-
9 s + 2 t = 22
_______________
- 4 s = - 16 Divide both sides by - 4
- 4 s / - 4 = - 16 / - 4
s = 4
5 s + 2 t = 6
5 * 4 + 2 t = 6
20 + 2 t = 6 Subtract 20 to both sides
20 + 2 t - 20 = 6 - 20
2 t = - 14 Divide both sides by 2
2 t / 2 = - 14 / 2
t = - 7
The solution ( 4 , - 7 )
4. Correct
5.
2 m - 5 n = - 6
-
2 m - 7 n = - 14
_______________
2 n = 8 Divide both sides by 2
2 n / 2 = 8 / 2
n = 4
______________________________________
Remark :
- 5 n - ( - 7 n ) = - 5 n + 7 n = 2 n
- 6 - ( - 14 ) = - 6 + 14 = 8
_______________________________________
2 m - 5 n = - 6
2 m - 5 * 4 = - 6
2 m - 20 = - 6 Add 20 to both sides
2 m - 20 + 20 = - 6 + 20
2 m = 14 Divide both sides by 2
2 m / 2 = 14 / 2
m = 7
The solution ( 7 , 4 )
6.
3 r - 5 s = - 35
-
2 r - 5 s = - 30
_______________
r = - 5
3 r - 5 s = - 35
3 * ( - 5 ) - 5 s = - 35
- 15 - 5 s = - 35 Add 15 to both sides
- 15 - 5 s + 15 = - 35 + 15
- 5 s = - 20 Divide both sides by - 5
- 5 s / - 5 = - 20 / -5
s = 4
The solution ( - 5 , 4 )
To check your answers, we need to substitute the values you obtained back into the original equations and see if they satisfy the equations.
1. x + y = 8
6 + 3 = 8 (True)
x - y = 4
6 - 3 = 4 (True)
So your solution (6, 3) is correct.
2. x - 3y = 7
4 - 3(-1) = 7 (True)
x + 2y = 2
4 + 2(-1) = 2 (True)
So your solution (4, -1) is correct.
3. 5s + 2t = 6
5(-4) + 2(13) = 6 (-20 + 26 = 6 is True)
9s + 2t = 22
9(-4) + 2(13) = 22 (-36 + 26 = 22 is True)
So your solution (-4, 13) is correct.
4. 2x + 3y = 13
2(5) + 3(1) = 13 (10 + 3 = 13 is True)
x - 3y = 2
5 - 3(1) = 2 (5 - 3 = 2 is True)
So your solution (5, 1) is correct.
5. 2m - 5n = -6
2(7) - 5(-4) = -6 (14 + 20 = -6 is False)
2m - 7n = -14
2(7) - 7(-4) = -14 (14 + 28 = -14 is False)
Your solution (7, -4) is incorrect.
6. 3r - 5s = -35
3r - 5s = -30 (Note: It seems like there was a mistake in the given equation)
Since the given equations are the same, they represent parallel lines and have no solution. Therefore, there is no solution for the system of equations.