To solve the system of equations:
5x + 7y = -3
3x + 4y = -2
You can use either the substitution method or the elimination method. Here is one way to solve the system using the elimination method:
Multiply both sides of the second equation by 7 to get:
21x + 28y = -14
Multiply both sides of the first equation by 4 to get:
20x + 28y = -12
Subtract the second equation from the first equation to eliminate y:
20x + 28y - (21x + 28y) = -12 - (-14)
-x = 2
Solve for x by dividing both sides by -1:
x = -2
Substitute x = -2 into either equation to solve for y. Using the first equation:
5(-2) + 7y = -3
-10 + 7y = -3
7y = 7
y = 1
Therefore, the solution to the system of equations is x = -2, y = 1.