Solve the equation 2x+3y=40 & 5x+2y=34.
Using elimination methods.
To solve this system of equations using elimination, first multiply the first equation by 5 and the second equation by 2 to make the coefficients of x in both equations equal:
(5)(2x + 3y) = 5(40)
10x + 15y = 200
(2)(5x + 2y) = 2(34)
10x + 4y = 68
Now, subtract the second equation from the first equation:
10x + 15y - 10x - 4y = 200 - 68
11y = 132
y = 12
Now, substitute y = 12 back into one of the original equations to solve for x. Let's use the first equation:
2x + 3(12) = 40
2x + 36 = 40
2x = 4
x = 2
Therefore, the solution to the system of equations is x = 2 and y = 12.