Problem 75
Question
Will help you prepare for the material covered in the first section of the next chapter. Is \((4,-1)\) a solution of both \(x+2 y=2\) and \(x-2 y=6 ?\)
Step-by-Step Solution
Verified Answer
Yes, the ordered pair (4, -1) is a solution for both given equations.
1Step 1: Substitute Coordinates Into First Equation
Plug x = 4 and y = -1 into the first equation x + 2y = 2. This gives 4 + 2(-1) = 4 - 2 = 2, so (4, -1) is a solution to the first equation.
2Step 2: Substitute Coordinates Into Second Equation
Next, substitute x = 4 and y = -1 into the second equation x - 2y = 6. This gives 4 - 2(-1) = 4 + 2 = 6, so (4, -1) is also a solution to the second equation.
3Step 3: Conclusions
Since (4, -1) is a solution to both equations, it is a solution to the system of equations.
Other exercises in this chapter
Problem 74
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