Final answer:
To find the values of x and y that satisfy the system of equations 10x - 2y = 18 and -10x + 9y = -46, we can use the method of substitution. The values of x and y that satisfy the system of equations are x = 9/5 and y = 28/11.
Step-by-step explanation:
To find the values of x and y that satisfy the system of equations 10x - 2y = 18 and -10x + 9y = -46, we can use the method of substitution. First, solve one equation for one variable in terms of the other variable. Let's solve the first equation for x in terms of y:
10x - 2y = 18 → 10x = 18 + 2y → x = (18 + 2y) / 10
Now substitute this value of x into the second equation:
-10((18 + 2y) / 10) + 9y = -46 → -18 - 2y + 9y = -46 → -11y = -46 + 18 → -11y = -28 → y = -28 / -11
Simplifying further, we find that y = 28/11. Now substitute this value of y back into the first equation to solve for x:
10x - 2(28/11) = 18 → 10x - 56/11 = 18 → 10x = 18 + 56/11 → 10x = 198/11 → x = 198/11 * 1/10 → x = 198/110 → x = 9/5
Therefore, the values of x and y that satisfy the system of equations are x = 9/5 and y = 28/11.