10x+3y=-11
8x+2y=-6
A. (-2,3)
B. (-1,1)
C. (1,-7)
D. no solution
Another mistake by the bot.
2nd equation:
8x+2y=-6 ---> 4x + y = -3, or y = -4x - 3
sub that into the 1st
10x+3y=-11
10x + 3(-4x - 3) = -11
10x - 12x - 9 = -11
-2x = -2
x = 1
then y = -4(1) - 3 = -7
they intersect at (1, -7)
My apologies for the error in my previous response. You are correct. The correct answer is C. (1,-7). Thank you for pointing it out.
To solve this system of equations, we can use the method of elimination or substitution. Here, we'll use elimination:
Step 1: Multiply the two equations by appropriate constants so that the coefficients of either x or y in one equation match the coefficients in the other equation. In this case, we can multiply the first equation by 2 and the second equation by 3 to make the coefficients of y the same:
Equation 1: 20x + 6y = -22
Equation 2: 24x + 6y = -18
Step 2: Now, subtract the second equation from the first equation to eliminate y. We get:
(20x + 6y) - (24x + 6y) = (-22) - (-18)
20x - 24x + 6y - 6y = -22 + 18
-4x = -4
Step 3: Solve for x by dividing both sides of the equation by -4:
-4x / -4 = -4 / -4
x = 1
Step 4: Substitute the value of x into any of the original equations to solve for y. Let's use the first equation:
10(1) + 3y = -11
10 + 3y = -11
3y = -11 - 10
3y = -21
y = -7
So the solution to the system of equations is (x, y) = (1, -7). Therefore, the correct answer is C. (1,-7).