how many solutions does these equations have
x + y = -7
-2x -2y =14
7 answers
These two equations have one solution.
you sure
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.
solve these equations by elimination
12x - 10y =2
-6x + 7y = -11
12x - 10y =2
-6x + 7y = -11
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.
ACTUAL ANSWER PLS
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.
1 answer