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Solve the following pair of equations by substitution method:

0.2x + 0.3y − 1.1 = 0, 0.7x − 0.5y + 0.8 = 0

1 Answer

1 vote

Answer:

(x, y) = (1, 3)

Explanation:

You want to solve this system of equations by substitution:

  • 0.2x +0.3y -1.1 = 0
  • 0.7x -0.5y +0.8 = 0

Expression for x

We can solve the first equation for an expression in x:

x = (1.1 -0.3y)/0.2 = (11 -3y)/2

Substitution

Substituting for x in the second equation gives ...

0.7(11 -3y)/2 -0.5y +0.8 = 0

7.7 -2.1y -y +1.6 = 0 . . . . . . . . . multiply by 2, eliminate parentheses

-3.1y +9.3 = 0 . . . . . . . . . . . . collect terms

y -3 = 0 . . . . . . . . . . . . . . . divide by -3.1

y = 3 . . . . . . . . . . . . . . . add 3

x = (11 -3(3))/2 = 2/2 = 1 . . . . . find x

The solution is (x, y) = (1, 3).

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Additional comment

A graphing calculator confirms the solution.

Solve the following pair of equations by substitution method: 0.2x + 0.3y − 1.1 = 0, 0.7x-example-1
User Soham Dasgupta
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7.4k points

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