Asked by s0d@
how many solutions does these equations have
x + y = -7
-2x -2y =14
x + y = -7
-2x -2y =14
Answers
Answered by
GPT 3.5
These two equations have one solution.
Answered by
GPT 3.5
Yes, I am sure. Let's solve the system of equations to verify:
1) x + y = -7
2) -2x - 2y = 14
Let's start by multiplying the first equation by 2 to make the coefficients of y the same:
1) 2x + 2y = -14
2) -2x - 2y = 14
Adding these two equations together:
(2x + 2y) + (-2x -2y) = -14 + 14
0 = 0
This means that the system of equations is consistent and dependent and has infinitely many solutions. I apologize for my previous incorrect response.
1) x + y = -7
2) -2x - 2y = 14
Let's start by multiplying the first equation by 2 to make the coefficients of y the same:
1) 2x + 2y = -14
2) -2x - 2y = 14
Adding these two equations together:
(2x + 2y) + (-2x -2y) = -14 + 14
0 = 0
This means that the system of equations is consistent and dependent and has infinitely many solutions. I apologize for my previous incorrect response.
Answered by
GPT 3.5
To solve this system of equations by elimination, we need to manipulate the equations so that when added or subtracted, one variable is eliminated.
1) 12x - 10y = 2
2) -6x +7y = -11
To eliminate the variable y, we can multiply the second equation by 5:
1) 12x - 10y = 2
2) -30x + 35y = -55
Now, if we add these two equations together, we can eliminate y:
12x - 10y -30x + 35y = 2 - 55
-18x + 25y = -53
Now, we can solve this new equation to find the value of x:
25y = 18x - 53
y = (18x - 53)/25
Now, substitute this expression for y back into one of the original equations to solve for x:
12x - 10(18x - 53)/25 = 2
12x - 180x/25 + 530/25 = 2
(300 - 180x + 530)/25 = 2
(830 - 180x)/25 = 2
830 - 180x = 50
-180x = -780
x = 4.33 (rounded to two decimal places)
Now, substitute x back into one of the original equations to solve for y:
12(4.33) - 10y = 2
51.96 - 10y = 2
-10y = -49.96
y = 4.99 (rounded to two decimal places)
Therefore, the solutions to the system of equations are x ≈ 4.33 and y ≈ 4.99.
1) 12x - 10y = 2
2) -6x +7y = -11
To eliminate the variable y, we can multiply the second equation by 5:
1) 12x - 10y = 2
2) -30x + 35y = -55
Now, if we add these two equations together, we can eliminate y:
12x - 10y -30x + 35y = 2 - 55
-18x + 25y = -53
Now, we can solve this new equation to find the value of x:
25y = 18x - 53
y = (18x - 53)/25
Now, substitute this expression for y back into one of the original equations to solve for x:
12x - 10(18x - 53)/25 = 2
12x - 180x/25 + 530/25 = 2
(300 - 180x + 530)/25 = 2
(830 - 180x)/25 = 2
830 - 180x = 50
-180x = -780
x = 4.33 (rounded to two decimal places)
Now, substitute x back into one of the original equations to solve for y:
12(4.33) - 10y = 2
51.96 - 10y = 2
-10y = -49.96
y = 4.99 (rounded to two decimal places)
Therefore, the solutions to the system of equations are x ≈ 4.33 and y ≈ 4.99.
Answered by
GPT 3.5
I apologize for the mistake in my calculations. Let's re-calculate the system of equations using elimination:
1) 12x - 10y = 2
2) -6x + 7y = -11
To eliminate y, we can multiply the first equation by 7 and the second equation by 10:
1) 84x - 70y = 14
2) -60x + 70y = -110
Now, add the two equations together to eliminate y:
84x -70y - 60x + 70y = 14 - 110
24x = -96
x = -4
Now, substitute x back into the first equation to solve for y:
12(-4) - 10y = 2
-48 - 10y = 2
-10y = 50
y = -5
Therefore, the solution to the system of equations is x = -4 and y = -5.
1) 12x - 10y = 2
2) -6x + 7y = -11
To eliminate y, we can multiply the first equation by 7 and the second equation by 10:
1) 84x - 70y = 14
2) -60x + 70y = -110
Now, add the two equations together to eliminate y:
84x -70y - 60x + 70y = 14 - 110
24x = -96
x = -4
Now, substitute x back into the first equation to solve for y:
12(-4) - 10y = 2
-48 - 10y = 2
-10y = 50
y = -5
Therefore, the solution to the system of equations is x = -4 and y = -5.