Choose the ordered pair that is a solution to the system of equations.
-x + y = 12
x + 2y = 3
a. (7, 5)
b. (5, -7)
c. (-7, 5)
d. (-7, -5)
e. none of the above
This question wants you to find the point of intersection of the two lines, provided they're not parallel.
Solve
-x + y = 12
x + 2y = 3
If you add them together you get
3y=15 so y=5, put that in either equation and solve for x. Try the first one
-x + 5 =12 so -x = 7 or x=-7
The point would be x=-7 and y=5
To solve the system of equations, you can use the method of elimination or substitution. Let's solve it using the method of elimination:
1. Start with the two equations:
-x + y = 12 ------(1)
x + 2y = 3 ------(2)
2. Multiply equation (1) by 2 to make the coefficients of x in both equations the same:
-2x + 2y = 24 ------(3)
3. Add equation (2) and equation (3) to eliminate the x term:
(x + 2y) + (-2x + 2y) = 3 + 24
0x + 4y = 27
4y = 27
y = 27/4
y = 6.75
4. Substitute the value of y back into equation (1) to solve for x:
-x + 6.75 = 12
-x = 12 - 6.75
-x = 5.25
x = -5.25
So, the solution to the system of equations is x = -5.25 and y = 6.75.
Now, let's check which ordered pair is a solution to the system:
a. (7, 5):
-7 + 5 ≠ 12 (not a solution)
b. (5, -7):
-5 + (-7) ≠ 12 (not a solution)
c. (-7, 5):
-(-7) + 5 = 12 (a solution)
d. (-7, -5):
-(-7) + (-5) ≠ 12 (not a solution)
Based on the above analysis, the correct answer is option (c) (-7, 5).