The system of equate rapned in the xy -plane.

Question

x + y = 1
2x - 3y = 17
Determine the coordinahow your volutions of the system algebraically. Then show that your solution is valid. Show your work or explain how you found your answers

Answer 1

To solve the system of equations algebraically, we can use the method of substitution.

First, let's solve the first equation for x in terms of y:
x + y = 1
x = 1 - y

Now substitute this value of x into the second equation:
2x - 3y = 17
2(1 - y) - 3y = 17
2 - 2y - 3y = 17
-5y = 15
y = -3

Now substitute this value of y back into the first equation to find x:
x + (-3) = 1
x = 4

Therefore, the solution to the system of equations is (x, y) = (4, -3).

To check the validity of this solution, we substitute the values of x and y into the original equations:

For the first equation:
4 + (-3) = 1
1 = 1 (True)

For the second equation:
2(4) - 3(-3) = 17
8 + 9 = 17
17 = 17 (True)

Both equations hold true when the values of x and y are substituted into them, confirming that the solution (x, y) = (4, -3) is valid.