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Chapter 3: Problem 75

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 \(x-2 y=6 ?\)

Short Answer

Expert verified
Yes, the ordered pair (4, -1) is a solution for both given equations.

Step by step solution

01

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.
02

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.
03

Conclusions

Since (4, -1) is a solution to both equations, it is a solution to the system of equations.

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Most popular questions from this chapter

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