what is the value of x in the solution to the system of equations below? 15x - 12y = 13.
30x + 9y = 4
To find the value of x in the solution to the system of equations, we can solve the equations using either substitution or elimination.
By elimination:
Multiply the second equation by 2 to make the coefficients of x in both equations cancel out:
30x + 9y = 4
(2)(30x) + (2)(9y) = (2)(4)
60x + 18y = 8
Now, subtract the first equation from this new equation:
60x + 18y - (15x - 12y) = 8 - 13
60x + 18y - 15x + 12y = -5
45x + 30y = -5
Simplify the equation:
15(3x + 2y) = -5
3x + 2y = -5/15
3x + 2y = -1/3
Now we can solve the system of equations:
15x - 12y = 13
3x + 2y = -1/3
Multiply the second equation by 5 to make the coefficients of y in both equations cancel out:
15x - 12y = 13
5(3x + 2y) = 5(-1/3)
15x + 10y = -5/3
Now, subtract the first equation from this new equation:
15x + 10y - (15x - 12y) = -5/3 - 13
15x + 10y - 15x + 12y = -5/3 - 39/3
22y = -44/3
y = (-44/3)/22
y = -2/3
Now substitute the value of y into any of the original equations:
15x - 12(-2/3) = 13
15x + 8 = 13
15x = 13 - 8
15x = 5
x = 5/15
x = 1/3
Therefore, the value of x in the solution to the system of equations is 1/3.