Can someone please check my work?
Solve using substitution method
1. 3x+2y=12
x=52-6y
answer:-40.8 I am pretty sure that one is wrong.
Solve using elimination method
2. 2r-7s=-31
7r+2s=24
answer: (230/53,-468/53)
3.3x+4y=3
6x+8y=6
answer: No answer. problems eliminate eachother
3(52-6y) + 2 y = 12
156 - 18 y + 2 y = 12
-16 y = -144
y = 9
x = 52 - 6(9) = 52 - 54 = -2
Thank you Damon!
Can you help me with the formula to solve by elimination?
3x+2y=12
x=52-6y multiply everything by 3 on this line
3x+2y=12
3 x = 156 - 18y
---------------- subtract
0 x + 2y = 12 -156 + 18 y
0 = - -144 + 16 y
y = 144/16 = 9 again
2r-7s=0
7r+2s=53
6,174,000,000
Sure, I can check your work for you.
1. To solve the system of equations using the substitution method, we substitute the value of x from one equation into the other equation.
Given equations:
1. 3x + 2y = 12
2. x = 52 - 6y
Let's substitute the value of x from equation 2 into equation 1:
3(52 - 6y) + 2y = 12
156 - 18y + 2y = 12
-16y = -144
y = 9
Now substitute the value of y back into equation 2 to find x:
x = 52 - 6(9)
x = -26
So the solution to the system of equations is (-26, 9). It seems the answer you provided, -40.8, is incorrect.
2. To solve the system of equations using the elimination method, we eliminate one variable by adding or subtracting the equations.
Given equations:
1. 2r - 7s = -31
2. 7r + 2s = 24
Multiply equation 1 by 7 and equation 2 by 2 to eliminate the r variable:
7(2r - 7s) = 7(-31)
14r - 49s = -217
2(7r + 2s) = 2(24)
14r + 4s = 48
Now, add the two equations together to eliminate the r variable:
(14r - 49s) + (14r + 4s) = -217 + 48
28r - 45s = -169
To solve for s, isolate the variable:
-45s = -169 - 28r
s = (-169 - 28r) / -45
Now substitute this expression for s back into one of the original equations (equation 1 or 2) to solve for r. Let's use equation 1:
2r - 7((-169 - 28r) / -45) = -31
Simplify the equation by multiplying through by -45 to eliminate the fraction:
-90r + 315 + 28r = -1395
-62r = -1710
r = (-1710) / -62
r = 105/31
Therefore, the solution to the system of equations is (230/53, -468/53), which is different from the answer you provided.
3. The third system of equations you provided is inconsistent and has no solution. This means the two equations contradict each other and cannot both be true at the same time.