Which ordered pair is a solution to the system of equations?
{4x+y=2
−2x+y=5
A. (1, -2)
B. (- 1/2, 4)
C. (2, -6)
D. (7/2, -12)
why not just solve the equation, they are perfectly set up.
subtract them:
6x = -3
x = -1/2
back in #1:
-2 + y = 2
y = 4
To determine which ordered pair is a solution to the system of equations, we need to substitute the values of the x-coordinate and y-coordinate into the equations and see if the equations are satisfied.
Let's go through each option and test it:
A. (1, -2)
Substituting x = 1 and y = -2 into the equations:
4(1) + (-2) = 2
-2(1) + (-2) = 5
Simplifying the equations:
4 - 2 = 2
-2 - 2 = 5
This option does not satisfy both equations.
B. (-1/2, 4)
Substituting x = -1/2 and y = 4 into the equations:
4(-1/2) + 4 = 2
-2(-1/2) + 4 = 5
Simplifying the equations:
-2 + 4 = 2
1 + 4 = 5
This option satisfies both equations.
C. (2, -6)
Substituting x = 2 and y = -6 into the equations:
4(2) + (-6) = 2
-2(2) + (-6) = 5
Simplifying the equations:
8 - 6 = 2
-4 - 6 = 5
This option does not satisfy both equations.
D. (7/2, -12)
Substituting x = 7/2 and y = -12 into the equations:
4(7/2) + (-12) = 2
-2(7/2) + (-12) = 5
Simplifying the equations:
14 + (-12) = 2
-7 + (-12) = 5
This option does not satisfy both equations.
Based on the tests, it can be concluded that option B, (-1/2, 4), is the solution to the system of equations.