Asked by Nicholai
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Part 1
Writing Solve the system using addition. Use pencil and paper. Explain why the addition method is a good choice for solving the system. If you wanted to solve for x first, is the addition method still a good choice? Explain.
x minus 3.6 y
equals
negative 9.4
negative x plus 4.4 y
equals
12.6
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Part 1
The solution is
enter your response here. (Type an ordered pair.)
All Answers 1
Answered by
GPT-5 mini
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Add the two equations:
x - 3.6y = -9.4
- x + 4.4y = 12.6
------------------
0 + 0.8y = 3.2 ⇒ y = 3.2 / 0.8 = 4.
Substitute y = 4 into the first equation:
x - 3.6(4) = -9.4 ⇒ x - 14.4 = -9.4 ⇒ x = 5.
Solution: (5, 4)
Why addition is a good choice: the x-coefficients (x and -x) are opposites, so adding the equations immediately eliminates x and gives a single equation in y.
If you wanted to solve for x first: you could still use the addition (elimination) method, but you would need to multiply the equations to make the y-coefficients opposites (extra steps and more arithmetic with decimals). So elimination still works but is less convenient in that direction; substitution might be simpler if you want x first.
x - 3.6y = -9.4
- x + 4.4y = 12.6
------------------
0 + 0.8y = 3.2 ⇒ y = 3.2 / 0.8 = 4.
Substitute y = 4 into the first equation:
x - 3.6(4) = -9.4 ⇒ x - 14.4 = -9.4 ⇒ x = 5.
Solution: (5, 4)
Why addition is a good choice: the x-coefficients (x and -x) are opposites, so adding the equations immediately eliminates x and gives a single equation in y.
If you wanted to solve for x first: you could still use the addition (elimination) method, but you would need to multiply the equations to make the y-coefficients opposites (extra steps and more arithmetic with decimals). So elimination still works but is less convenient in that direction; substitution might be simpler if you want x first.
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