Question

Solve the system of equations by the addition method. If a system contains​ decimals, you may want to first clear the equation of decimals.

1.3x + 0.5y = 17
-0.7 - 2.5y = -73.4

Answer 1

Answer:x = 2

y = 28.8

Explanation:

The given system of simultaneous equations is expressed as

1.3x + 0.5y = 17 - - - - - - - - - - - - 1

-0.7 - 2.5y = -73.4 - - - - - - - - - - - - - 2

The first step multiply all the terms by 10 in order to eliminate the decimal points. The equations become

13x + 5y = 170 - - - - - - - - - - - - 1

-7 - 25y = -734 - - - - - - - - - - - - - 2

Then we would multiply both rows by numbers which would make the coefficients of x to be equal in both rows.

Multiplying equation 1 by 7 and equation 2 by 13, it becomes

91x + 35y = - 1190

91x + 325y = 9542

Subtracting, it becomes

- 290y = - 8352

y = - 8352/- 290 = 28.8

Substituting y = 28.8 into equation 1, it becomes

13x + 5 × 28.8 = 170

13x + 144 = 170

13x = 170 - 144 = 26

x = 26/13 = 2

Answer 2

(x, y) = (2, 28.8)

Explanation:

Your ability to do arithmetic should not be limited to integers. Here we see the coefficients of y are related by a factor of -5, so multiplying the first equation by 5 can make the y-terms cancel when that is added to the second equation.

5(1.3x +0.5y) +(-0.7x -2.5y) = 5(17) +(-73.4)

6.5x +2.5y -0.7x -2.5y = 85 -73.4 . . . . . eliminate parentheses

5.8x = 11.6 . . . . . . collect terms

x = 11.6/5.8 = 2 . . . . . . . divide by the coefficient of x

1.3(2) +0.5y = 17 . . . . . . substitute for x in the first equation

0.5y = 14.4 . . . . . . subtract 2.6

y = 28.8 . . . . . . . . multiply by 2

The solution is (x, y) = (2, 28.8).