Solve the system of two linear equations.
-3x - 4y = - 23
3x -5y = 5
A. (-5, 2)
B. (5, -2)
C. (5, 2)
D. (-5, -2)
To solve the system of equations, we can use the method of substitution or the method of elimination. Let's use the method of substitution.
First, solve one of the equations for one variable and substitute it into the other equation. Let's solve the first equation for x:
-3x - 4y = -23
Add 4y to both sides:
-3x = 4y - 23
Divide both sides by -3:
x = (4y - 23)/-3
Now, substitute this expression for x in the second equation:
3x - 5y = 5
3((4y - 23)/-3) - 5y = 5
Cancel out the -3 and the 3:
4y - 23 - 5y = 5
Combine like terms:
-y - 23 = 5
Add 23 to both sides:
-y = 28
Multiply both sides by -1 to isolate y:
y = -28
Now substitute this value of y back into the expression for x:
x = (4(-28) - 23)/-3
x = (-112 - 23)/-3
x = -135/-3
x = 45
Therefore, the solution to the system of equations is (45, -28). None of the answer choices match this solution, so none of the answer choices are correct.
NOT AN ANSWER
Apologies for the incorrect response. Let's solve the system of equations correctly.
We have the equations:
-3x - 4y = -23 ........... (1)
3x - 5y = 5 .............. (2)
To eliminate one variable, let's multiply equation (2) by -1:
-3x - 4y = -23 ........... (1)
-3x + 5y = -5 ............ (3)
By subtracting equation (1) from equation (3), we can eliminate x:
(-3x - 4y) - (-3x + 5y) = (-23) - (-5)
-3x - 4y + 3x - 5y = -23 + 5
-9y = -18
Divide both sides of the equation by -9:
y = 2
Substitute the value of y in equation (1):
-3x - 4(2) = -23
-3x - 8 = -23
-3x = -23 + 8
-3x = -15
Divide both sides of the equation by -3:
x = -15 / -3
x = 5
Therefore, the solution to the system of equations is (5, 2), which matches answer choice C.
omg give me an answer from what i listed
Apologies for the confusion. Let's solve the system of equations using the given answer choices.
The system of equations is:
-3x - 4y = -23 ........... (1)
3x - 5y = 5 .............. (2)
The answer choices are:
A. (-5, 2)
B. (5, -2)
C. (5, 2)
D. (-5, -2)
We can substitute the values from each answer choice into both equations to see which one satisfies both equations:
A. (-5, 2)
Substituting into equation (1):
-3(-5) - 4(2) = -23
15 - 8 = -23
7 = -23 (not true)
Substituting into equation (2):
3(-5) - 5(2) = 5
-15 - 10 = 5
-25 = 5 (not true)
B. (5, -2)
Substituting into equation (1):
-3(5) - 4(-2) = -23
-15 + 8 = -23
-7 = -23 (not true)
Substituting into equation (2):
3(5) - 5(-2) = 5
15 + 10 = 5
25 = 5 (not true)
C. (5, 2)
Substituting into equation (1):
-3(5) - 4(2) = -23
-15 - 8 = -23
-23 = -23 (true)
Substituting into equation (2):
3(5) - 5(2) = 5
15 - 10 = 5
5 = 5 (true)
D. (-5, -2)
Substituting into equation (1):
-3(-5) - 4(-2) = -23
15 + 8 = -23
23 = -23 (not true)
Substituting into equation (2):
3(-5) - 5(-2) = 5
-15 + 10 = 5
-5 = 5 (not true)
Thus, the solution to the system of equations is (5, 2), which matches answer choice C.
To solve the system of two linear equations, we can use the method of elimination.
Step 1: Multiply the second equation by 2 to make the coefficients of x in both equations cancel out:
2(3x - 5y) = 2(5)
6x - 10y = 10
Step 2: Now we have two equations:
-3x - 4y = - 23
6x - 10y = 10
Step 3: Add the two equations together to eliminate the variable x:
(-3x - 4y) + (6x - 10y) = (-23) + (10)
3x - 14y = -13
Step 4: Solve the new equation for y:
-14y = -13 - 3x
14y = 3x + 13
y = (3/14)x + 13/14
Step 5: Substitute the value of y into one of the original equations:
-3x - 4(3/14)x - 4(13/14) = -23
-3x - (12/14)x - (52/14) = -23
-3x - (6/7)x - (26/7) = -23
-21x - 6x - 26 = -161
-27x - 26 = -161
-27x = -161 + 26
-27x = -135
x = (-135) / (-27)
x = 5
Step 6: Substitute the value of x back into y = (3/14)x + 13/14 to find y:
y = (3/14)(5) + 13/14
y = 15/14 + 13/14
y = 28/14
y = 2
Therefore, the solution to the system of equations is (x, y) = (5, 2)
So, the correct answer is:
C. (5, 2)
To solve the system of two linear equations, we can use the method of elimination or substitution. Let's solve it using the elimination method.
Step 1: Multiply the second equation by -1 to eliminate the x-term.
-3x - 4y = -23
-1(3x - 5y) = -1(5)
-3x + 5y = -5
Step 2: Add the two equations together to eliminate the x-term.
(-3x - 4y) + (-3x + 5y) = (-23) + (-5)
-6x + y = -28 --> Equation (1)
Step 3: Solve one of the equations for one variable.
From the first equation, we can solve for x:
-3x - 4y = -23
-3x = 23 - 4y
x = (23 - 4y)/(-3)
Step 4: Substitute the expression for x in Equation (1).
-6((23 - 4y)/(-3)) + y = -28
Step 5: Simplify and solve for y.
46 - 8y + 3y = -84
46 - 5y = -84
-5y = -84 - 46
-5y = -130
y = -130/(-5)
y = 26
Step 6: Substitute the value of y into the expression for x.
x = (23 - 4(26))/(-3)
x = (23 - 104)/(-3)
x = -81/(-3)
x = 27
Therefore, the solution to the system of equations is (27, 26).
Comparing this solution to the options given, none of the answer choices matches the solution, so none of the given options are correct.