Solve the system of equations.
−4x+6y=38
x−5y=−20 (1 point)
Responses
(5, 3)
left parenthesis 5 comma 3 right parenthesis
(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis
(−35, −3)
left parenthesis negative 35 comma negative 3 right parenthesis
(35, −3)
(5, 3)
To solve the system of equations:
−4x + 6y = 38 (equation 1)
x − 5y = −20 (equation 2)
We can solve this system using the method of substitution or elimination. I will use the method of substitution.
Step 1: Solve equation 2 for x in terms of y.
x = 5y - 20
Step 2: Substitute the value of x in equation 1 with the expression obtained in step 1.
-4(5y - 20) + 6y = 38
Step 3: Simplify and solve for y.
-20y + 80 + 6y = 38
-14y + 80 = 38
-14y = 38 - 80
-14y = -42
y = (-42) / (-14)
y = 3
Step 4: Substitute the value of y back into equation 2 to find the value of x.
x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5
Therefore, the solution to the system of equations is (x, y) = (-5, 3).
To solve the system of equations, we can use either the substitution or elimination method. I'll explain how to solve it using the elimination method.
1. Multiply the second equation by 4 so that the coefficients of x in both equations will cancel each other out when added together:
Original equations:
-4x + 6y = 38 (equation 1)
x - 5y = -20 (equation 2)
Multiply equation 2 by 4:
4(x - 5y) = 4(-20)
4x - 20y = -80 (new equation 2)
2. Add the two equations together to eliminate x:
-4x + 6y + 4x - 20y = 38 - 80
-14y = -42
y = -42 / -14
y = 3
3. Substitute the value of y back into either of the original equations to solve for x:
-4x + 6(3) = 38
-4x + 18 = 38
-4x = 38 - 18
-4x = 20
x = 20 / -4
x = -5
Therefore, the solution to the system of equations is x = -5 and y = 3. So, the correct answer is (−5, 3).