Solve the system of two linear equations. −3x−4y=−23 3x−5y=5 (1 point) Responses (−5, 2) left parenthesis negative 5 comma 2 right parenthesis (5, 2) left parenthesis 5 comma 2 right parenthesis (−5,−2) left parenthesis negative 5 comma negative 2 right parenthesis (5,−2)

Answer 1

To solve the given system of linear equations:

1) Multiply the second equation by 2 to make the x coefficients cancel out when summed.

-3x - 4y = -23
2(3x - 5y) = 2(5)
-3x - 4y = -23
6x - 10y = 10

2) Add the two equations together to eliminate the x terms.

-3x - 4y + 6x - 10y = -23 + 10
3x - 4y = -13

3) Solve the resulting equation for y.

-4y = -13 - 3x
y = (-13-3x)/(-4)

4) Substitute the value of y into one of the original equations to solve for x.

-3x - 4((-13-3x)/(-4)) = -23
-3x + 13 + 3x = -23
13 = -23

The resulting equation is a contradiction (13 does not equal -23), meaning there is no solution to the given system of equations.