Question

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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 2.8 y
equals
9.4
negative x plus 2.2 y
equals
negative 7.6
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Part 1
The solution is
  
enter your response here. ​(Type an ordered​ pair.)

Answer 1

Add the two equations:
x - 2.8y = 9.4
-(x) + 2.2y = -7.6
--------------------------------
0x + (-0.6y) = 1.8 ⇒ -0.6y = 1.8 ⇒ y = -3.

Substitute y = -3 into x - 2.8y = 9.4:
x - 2.8(-3) = 9.4 ⇒ x + 8.4 = 9.4 ⇒ x = 1.

Solution: (1, -3).

Why addition is a good choice: the x-coefficients are opposites (x and -x), so adding immediately eliminates x and gives a single equation in y. If you wanted to solve for x first you could use addition, but you'd need to multiply the equations first to make the y-coefficients opposites (more work). So addition is still possible but less convenient for solving x first.