Question

solve by useing elimination.
6x + 5y = 3
2x + 3y = 13

Answer 1

To solve this system of equations using elimination, we want to eliminate one of the variables by manipulating the equations.

We can eliminate the variable y by multiplying the first equation by 3 and the second equation by 5, so that we can get the same coefficients for y in both equations.

3*(6x + 5y) = 3*(3)
5*(2x + 3y) = 5*(13)

18x + 15y = 9
10x + 15y = 65

Now, we can subtract the second equation from the first equation to eliminate the variable y:

(18x + 15y) - (10x + 15y) = 9 - 65
18x - 10x + 15y - 15y = -56
8x = -56
x = -56/8
x = -7

Now, substitute x = -7 into one of the original equations to solve for y:

6(-7) + 5y = 3
-42 + 5y = 3
5y = 3 + 42
5y = 45
y = 45/5
y = 9

Therefore, the solution to the system of equations is x = -7 and y = 9.