solve the system with elimination 2x+5y=13 and -4x-3y=9
To solve the system of equations using elimination, we can multiply the first equation by 4 and the second equation by 2 to make the coefficients of x in both equations cancel each other out.
4(2x + 5y) = 4(13) (multiply the first equation by 4)
-2(-4x - 3y) = -2(9) (multiply the second equation by 2)
This simplifies to:
8x + 20y = 52
8x + 6y = -18
Now, we can subtract the second equation from the first equation to eliminate x:
(8x + 20y) - (8x + 6y) = 52 - (-18)
8x - 8x + 20y - 6y = 52 + 18
14y = 70
Divide both sides of the equation by 14:
y = 70/14
y = 5
Now, substitute the value of y back into one of the original equations, such as the first equation:
2x + 5(5) = 13
2x + 25 = 13
2x = 13 - 25
2x = -12
x = -12/2
x = -6
Therefore, the solution to the system of equations is x = -6 and y = 5.