Solve the system of equations. −4x+6y=38 x−5y=−20 (1 point) Responses (−5, 3) left parenthesis negative 5 comma 3 right parenthesis (5, 3) left parenthesis 5 comma 3 right parenthesis (35, −3) left parenthesis 35 comma negative 3 right parenthesis (−35, −3)

Answer 1

To solve the system of equations, we can use the method of substitution. We will solve equation 2 for x and substitute it into equation 1.

From equation 2:
x-5y = -20
x = 5y - 20

Now we substitute it into equation 1:
-4x + 6y = 38
-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y + 80 = 38
-14y = -42
y = 3

Substitute the value of y into equation 2 to find x:
x - 5(3) = -20
x - 15 = -20
x = -5

So the solution to the system of equations is (-5, 3). Answer: (-5, 3)

Answer 2

How many solution(s) does the system of equations have? −5x+y=−18 10x−2y=36 (1 point) Responses none none two two one one infinite

Answer 3

To determine the number of solutions the system of equations has, we can use the method of elimination. We will multiply equation 1 by 2 and add it to equation 2 to eliminate the y variable.

2 * (-5x + y) = 2 * (-18)
-10x + 2y = -36

Adding the equations together:
-10x + 2y + 10x - 2y = -36 + 36
0 = 0

Since 0 = 0, this means that the two equations are equivalent. Therefore, the system of equations has infinitely many solutions. Answer: infinite.