Question

Solve the following system of equations 2.5x-1.9y=4.9 -0.5x+1.8y=4.7

Answer 1

To solve the system of equations
`\left \{ {{2.5x - 1.9y=4.9} \atop {-0.5x+1.8y=4.7}} \right.`, we first need to solve for x in terms of y (this solution shall use the first equation, but neither equation is better).

2.5x - 1.9y = 4.9

2.5x = 1.9y + 4.9

x =
`(49+19y)/(25)`

Now, we can substitute this value of x in the second equation.

-0.5(
`(49+19y)/(25)`) + 1.8y = 4.7

`(49+19y)/(50)` + 1.8y = 4.7

To make solving this equation easier for ourselves, we can multiple all of these terms by their denominator's least common multiple, 50.

-49 - 19y + 90y = 235

71y = 284

y = 4

Now we can substitute the value of y into the value of x (the big fraction).

x =
`(49+19(4))/(25)` =
`(125)/(25)` = 5

That means that the solution to this system of equations is (5, 4)

Answer 2

2.5x-1.9y=4.9

-0.5x+1.8y=4.7 Multiply this equation by 5 to obtain a first term of -2.5x:

-2.5x + 9y = 23.5 To this version of the 1st equation add the entire 2nd equation:

-2,5x + 9y = 23.5

2.5x -1.9y = 4.9

------------------------- Combine these two equations, which will eliminate x:

7.1y = 28.4 Now divide both sides by 7.1 to obtain a value for y:

y = 28.4 / 7.1 = 4

Now substitute 4 for y in either of the original equations:

2.5x - 1.9(4) = 4.9, or 2.5x = 12.5. Sovling for x, x = 12.5 / 2.5 = 5.

Then the solution is (4, 5).