Question

Which ordered pair is a solution of the linear system? $$ \begin{aligned} &x+y=0.5\\\ &x+2 y=1 \end{aligned} $$ \(\begin{array}{llll}\text { (A) }(0,-2) & \text { (B) }(-0.5,0) & \text { C } & (0,0.5)\end{array}\) (D) \((0,-0.5)\)

Short answer

The solution to the given linear system of equations is ordered pair (C) (0, 0.5).

Step-by-step solution

Substitute (A) into both equations

Substitute ordered pair (A) \( (0, -2) \) into the equations as follows: \n In the first equation, replace \(x\) with 0 and \(y\) with -2: \(0 - 2 = -2\), not equal to 0.5. Therefore, (0, -2) is not a solution to the system.

Substitute (B) into both equations

Substitute ordered pair (B) \(-0.5,0\) into the equations. Replace \(x\) with -0.5 and \(y\) with 0 in both the equations: \n In the first equation, -0.5 + 0 = -0.5, which is not equal to 0.5. Therefore, (-0.5, 0) is not a solution to the system.

Substitute (C) into both equations

Now, substitute ordered pair (C) (0, 0.5) into the equations. Replace \(x\) with 0 and \(y\) with 0.5: \n In the first equation, 0 + 0.5 = 0.5, and in the second equation, 0 + 2 * 0.5 = 1. Both equal the respective constants from the equations. Therefore, (0, 0.5) is a solution to the system.

No need to substitute (D)

Given that multiple choice questions have only one correct answer and we have already found that (C) (0, 0.5) is a valid solution, there is no need to test the fourth option.