Solve the system of two linear equations.
−3x−4y=−23
3x−5y=5 (1 point)
Responses
(5, 2)
left parenthesis 5 comma 2 right parenthesis
(5,−2)
left parenthesis 5 comma negative 2 right parenthesis
(−5, 2)
left parenthesis negative 5 comma 2 right parenthesis
(−5,−2)
(5, 2)
or
left parenthesis 5 comma 2 right parenthesis
To solve the system of equations -3x - 4y = -23 and 3x - 5y = 5, we can use the method of elimination.
First, let's multiply the second equation by -1 to eliminate the x term:
-1*(3x - 5y) = -1*5
-3x + 5y = -5
Now, add the two equations together:
(-3x - 4y) + (-3x + 5y) = -23 + (-5)
-6x + y = -28
Next, isolate the y variable by adding 6x to both sides:
-6x + y + 6x = -28 + 6x
y = -28 + 6x
Then, substitute this expression for y into one of the original equations. Let's use the first equation:
-3x - 4(-28 + 6x) = -23
Simplify the equation:
-3x + 112 - 24x = -23
-27x + 112 = -23
Now, isolate the x variable by subtracting 112 from both sides:
-27x = -23 - 112
-27x = -135
Divide both sides by -27 to solve for x:
x = -135 / -27
x = 5
Substitute this value of x back into the expression for y:
y = -28 + 6x
y = -28 + 6(5)
y = -28 + 30
y = 2
Therefore, the solution to the system of equations is (5, 2).
To solve the system of two linear equations, we can use the method of substitution or the method of elimination. Let's use the method of substitution.
We have the following system of equations:
-3x - 4y = -23 ...(Equation 1)
3x - 5y = 5 ...(Equation 2)
Step 1: Solve Equation 1 for x.
To isolate x in Equation 1, we can add 4y to both sides:
-3x = 4y - 23
Next, divide both sides by -3:
x = (4y - 23)/-3 ...(Equation 3)
Step 2: Substitute Equation 3 into Equation 2.
Now that we have the value of x in terms of y, we can substitute Equation 3 into Equation 2.
3((4y - 23)/-3) - 5y = 5
Multiplying both sides by -3 to get rid of the fractions:
4y - 23 - 5y = -15
Combining like terms:
-y - 23 = -15 ...(Equation 4)
Step 3: Solve Equation 4 for y.
To isolate y in Equation 4, we can add 23 to both sides:
-y = -15 + 23
Simplifying:
-y = 8
Multiplying both sides by -1 to solve for y:
y = -8
Step 4: Substitute the value of y back into Equation 3 to solve for x.
Using Equation 3:
x = (4(-8) - 23)/-3
x = (-32 - 23)/-3
x = -55/-3
x = 55/3
Therefore, the solution to the system of linear equations is (55/3, -8).
Please note that the given answer choices in the responses do not match the correct solution (55/3, -8).