To solve the system of equations [tex] \left \{ {{2.5x - 1.9y=4.9} \atop {-0.5x+1.8y=4.7}} \right. [/tex], 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 = [tex] \frac{49+19y}{25} [/tex]
Now, we can substitute this value of x in the second equation.
-0.5([tex] \frac{49+19y}{25} [/tex]) + 1.8y = 4.7
[tex] \frac{49+19y}{50} [/tex] + 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 = [tex] \frac{49+19(4)}{25} [/tex] = [tex] \frac{125}{25} [/tex] = 5
That means that the solution to this system of equations is (5, 4)
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).
