Solve the system of two linear equations.
−3x−4y=−23
3x−5y=5
responses
(5,−2)
(5, 2)
(−5,−2)
(−5, 2)
To solve the system of equations, we can use the method of elimination.
First, let's add the two equations together to eliminate the x terms:
(-3x - 4y) + (3x - 5y) = -23 + 5
-7y = -18
Next, divide both sides of the equation by -7 to solve for y:
y = 18/7
Now, substitute the value of y back into one of the original equations to solve for x. Let's use the second equation:
3x - 5(18/7) = 5
3x - 90/7 = 5
Next, let's solve for x by isolating it:
3x = 5 + 90/7
3x = 35/7 + 90/7
3x = 125/7
Now, divide both sides of the equation by 3 to solve for x:
x = (125/7) * (1/3)
x = 125/21
So the solution to the system of equations is (125/21, 18/7), which can be approximated as (5.95, 2.57).
Therefore, the correct response is (5, 2).
To solve the system of equations −3x−4y=−23 and 3x−5y=5, we can use the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other.
Let's solve the second equation for x:
3x − 5y = 5
3x = 5 + 5y
x = (5 + 5y) / 3
Step 2: Substitute the expression for x into the other equation.
Substitute (5 + 5y) / 3 for x in the first equation:
−3((5 + 5y) / 3) − 4y = −23
Simplify:
−5 − 5y − 4y = −23
−9y - 5 = -23
−9y = -23 + 5
−9y = -18
y = -18 / -9
y = 2
Step 3: Substitute the value of y back into either of the original equations to solve for x.
Using the second equation:
3x − 5(2) = 5
3x − 10 = 5
3x = 5 + 10
3x = 15
x = 15 / 3
x = 5
Therefore, the solution to the system of equations is (5, 2).
To solve the system of linear equations:
−3x − 4y = −23 ..............(1)
3x − 5y = 5 ..............(2)
There are several methods to solve this system of linear equations, but I'll explain one common method known as the "substitution method".
Step 1: Solve one equation for one variable in terms of the other variable.
We can choose equation (1) to solve for x:
−3x − 4y = −23
First, let's isolate x by moving the term containing y to the other side of the equation:
−3x = 4y - 23
Now, divide both sides of the equation by -3 to solve for x:
x = (4y - 23)/(-3)
x = (23 - 4y)/3 ..............(3)
Step 2: Substitute the expression for x obtained in step 1 into the other equation.
Substitute equation (3) into equation (2):
3((23 - 4y)/3) − 5y = 5
Now simplify the equation:
23 - 4y − 5y = 5
23 - 9y = 5
Step 3: Solve for y.
To solve for y, we need to isolate the variable. Move the constant term to the other side:
-9y = 5 - 23
-9y = -18
To get the value of y, divide both sides by -9:
y = -18 / -9
y = 2
Step 4: Substitute the value of y back into equation (3) to find x.
Using equation (3):
x = (23 - 4(2))/3
x = (23 - 8)/3
x = 15/3
x = 5
The solution to the system of linear equations is (5, 2).