−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) left parenthesis 5 comma negative 2 right parenthesis

Answer 1

To solve this system of equations, we can use the method of elimination. If we multiply the first equation by 3 and the second equation by -3, we can eliminate the term '3x' by adding the two equations together:

(3 * (-3x - 4y) = 3 * (-23)) which becomes -9x - 12y = -69
(-3 * (3x - 5y) = -3 * 5) which becomes -9x + 15y = -15

Adding the above two equations together, we get:
(-9x - 12y) + (-9x + 15y) = -69 + (-15)
-9x - 9x - 12y + 15y = -69 - 15
-18x + 3y = -84

Now, let's multiply the second equation by 4, so we can eliminate the term '3y'.
4 * (3x - 5y) = 4 * 5 which becomes 12x - 20y = 20

Adding the above equation to -18x + 3y = -84, we get:
(12x - 20y) + (-18x + 3y) = 20 + (-84)
12x - 18x - 20y + 3y = 20 - 84
-6x - 17y = -64

Now, we have the two equations:
-18x + 3y = -84
-6x - 17y = -64

To eliminate the term '3y', we can multiply the first equation by 17 and the second equation by 3:
17 * (-18x + 3y) = 17 * (-84) which becomes -306x + 51y = -1428
3 * (-6x - 17y) = 3 * (-64) which becomes -18x - 51y = -192

Adding the above equations together, we get:
(-306x + 51y) + (-18x - 51y) = -1428 + (-192)
-306x - 18x + 51y - 51y = -1428 - 192
-324x = -1620

Dividing both sides of the equation by -324, we obtain:
x = 5

Now, we can substitute the value of x into one of the original equations to solve for y. Let's substitute x = 5 into the second equation:
3x - 5y = 5
3(5) - 5y = 5
15 - 5y = 5
-5y = -10
y = 2

The solution to the system of equations is (x, y) = (5, 2), so the answer is choice (5, 2).