The system of equate rapned in the xy -plane.
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
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.