Solve the system of two linear equations. −3x−4y=−23 3x−5y=5 (1 point) Responses (−5,−2) left parenthesis negative 5 comma negative 2 right parenthesis (5, 2) left parenthesis 5 comma 2 right parenthesis (−5, 2) left parenthesis negative 5 comma 2 right parenthesis (5,−2) left parenthesis 5 comma negative 2 right parenthesis
To solve this system of equations by elimination, we can add the two equations together to eliminate the variable x:
(-3x - 4y) + (3x - 5y) = -23 + 5
-3x + 3x - 4y - 5y = -18
-9y = -18
y = 2
Substituting this value of y into one of the original 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).
To solve the system of linear equations:
-3x - 4y = -23 (Equation 1)
3x - 5y = 5 (Equation 2)
We can solve this system by either substitution or elimination method.
Let's use the elimination method to solve it:
Multiply Equation 1 by 3 and Equation 2 by -3 to eliminate the x variable:
-9x - 12y = -69 (Multiply Equation 1 by 3)
-9x + 15y = -15 (Multiply Equation 2 by -3)
Add the two equations together:
(-9x - 12y) + (-9x + 15y) = -69 + (-15)
-18y = -84
Divide both sides of the equation by -18:
y = (-84) / (-18)
y = 4.67 (rounded to two decimal places)
Now substitute the value of y into Equation 1 to find the value of x:
-3x - 4(4.67) = -23
-3x - 18.68 = -23
-3x = -23 + 18.68
-3x = -4.32
Divide both sides of the equation by -3:
x = (-4.32) / (-3)
x = 1.44 (rounded to two decimal places)
So the solution to the system of linear equations is (1.44, 4.67)
To solve the system of two linear equations, −3x−4y=−23 and 3x−5y=5, we can use the method of substitution or the method of elimination. I will demonstrate the method of elimination.
Step 1: Multiply the second equation by 3 to make the x coefficients the same.
Original system:
−3x − 4y = −23 (Equation 1)
3x − 5y = 5 (Equation 2)
Multiply Equation 2 by 3:
9x − 15y = 15 (Equation 3)
Step 2: Add Equation 1 and Equation 3 to eliminate the x variable.
Adding Equation 1 and Equation 3:
(-3x - 4y) + (9x - 15y) = (-23) + (15)
6x - 19y = -8 (Equation 4)
Step 3: Solve Equation 4 for y.
Solving Equation 4 for y:
6x -19y = -8
-19y = -6x - 8
y = (-6x - 8) / -19
y = (6x + 8) / 19 (Equation 5)
Step 4: Substitute Equation 5 into Equation 1 and solve for x.
Substituting Equation 5 into Equation 1:
-3x - 4((6x + 8) / 19) = -23
-3x - 24x/19 - 32/19 = -23
(-57x - 24x - 32) / 19 = -23
-81x - 32 = -437
-81x = -437 + 32
-81x = -405
x = (-405) / (-81)
x = 5
Step 5: Substitute the value of x into Equation 5 and solve for y.
Substituting x=5 into Equation 5:
y = (6(5) + 8) / 19
y = (30 + 8) / 19
y = 38/19
y = 2
Therefore, the solution to the system of equations is (5, 2).