Solve the system of two linear equations. −3x−4y=−23 3x−5y=5 (1 point) Responses (5, 2) (−5, 2) (5,−2) (−5,−2)
To solve the system of equations, we can use the method of elimination or substitution.
Using elimination, we can add the two equations together to eliminate the x term:
(-3x - 4y) + (3x - 5y) = -23 + 5
-9y = -18
y = 2
Substituting y = 2 into one of the equations, we can solve for x:
3x - 5(2) = 5
3x - 10 = 5
3x = 15
x = 5
Therefore, the solution to the system of equations is (5, 2). Answer: \boxed{(5, 2)}.
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To solve the system of two linear equations:
Equation 1: -3x - 4y = -23
Equation 2: 3x - 5y = 5
We can use the method of substitution to find the values of x and y.
Step 1: Solve Equation 1 for x:
-3x - 4y = -23
-3x = 4y - 23
x = (4y - 23) / -3
Step 2: Substitute the value of x from Step 1 into Equation 2:
3((4y - 23) / -3) - 5y = 5
4y - 23 - 5y = 5
-y - 23 = 5
-y = 5 + 23
-y = 28
y = -28
Step 3: Substitute the value of y from Step 2 into Equation 1:
-3x - 4(-28) = -23
-3x + 112 = -23
-3x = -23 - 112
-3x = -135
x = (-135) / -3
x = 45
Therefore, the solution to the system of linear equations is (x, y) = (45, -28).
To solve the system of linear equations:
1. We will use the method of elimination to eliminate one variable and solve for the other.
2. Multiply the first equation by 3 and the second equation by -3 to make the x-coefficients cancel each other out when we add the equations together.
-9x - 12y = -69
-9x +15y = -15
3. Add the equations together:
(-9x - 12y) + (-9x + 15y) = (-69) + (-15)
-18y = -84
4. Divide both sides of the equation by -18:
y = (-84) / (-18)
y = 4.666667 or approximately 4.67
5. Now substitute the value of y back into one of the original equations. Let's use the first equation:
-3x - 4(4.67) = -23
-3x - 18.68 = -23
6. Add 18.68 to both sides of the equation:
-3x = -23 + 18.68
-3x = -4.32
7. Divide both sides of the equation by -3:
x = (-4.32) / (-3)
x = 1.44
8. Therefore, the solution to the system of equations is (x, y) = (1.44, 4.67).
So, the correct answer is (1.44, 4.67).