Final answer:
To find the solution to the system of equations 5x-2y=-11 and -2x+5y=17, we can use the method of substitution or elimination. Let's use the method of substitution. The solution to the system of equations is x = -284/29 and y = 107/29.
Step-by-step explanation:
To find the solution to the system of equations 5x-2y=-11 and -2x+5y=17, we can use the method of substitution or elimination. Let's use the method of substitution. First, solve one equation for one variable:
From the second equation, we can solve for x:
-2x + 5y = 17
-2x = 17 - 5y
x = (17 - 5y)/(-2)
Now substitute the value of x into the first equation:
5x - 2y = -11
5((17 - 5y)/(-2)) - 2y = -11
Solve for y:
85 - 25y - 4y = -22
-29y = -107
y = -107/-29
y = 107/29
Substitute the value of y back into the equation for x:
x = (17 - 5(107/29))/(-2)
x = -284/29
Therefore, the solution to the system of equations is x = -284/29 and y = 107/29.