Answer:
(x, y) = (16/3, -1/9)
Step-by-step explanation:
A system of two linear equations can be solved a number of ways. One of the easiest is by graphing. Algebraic methods usually work better when the equations are in standard or general form.
Graph
A graphing calculator can work with the given equations. The solution it shows in the first attachment is ...
(x, y) = (16/3, -1/9)
Algebraic method
An algebraic method of solving a pair of linear equations can start with them in general form. We can obtain that form by subtracting one side of the equation from both sides. Here, we choose to do that so the coefficient of x is positive.
First equation
5(x -3y) -6 -(4x +1) = 0 . . . . . . . subtract (4x+1) from both sides
5x -15y -6 -4x -1 = 0 . . . . . . eliminate parentheses
x -15y -7 = 0 . . . . . . . . . . collect terms
Second equation
3(x +6y) +4 -(9y +19) = 0 . . . . . . subtract (9y+19) from both sides
3x +18y +4 -9y -19 = 0 . . . . . . eliminate parentheses
3x +9y -15 = 0 . . . . . . . . . . . collect terms
x +3y -5 = 0 . . . . . . . . . . . remove common factor of 3
We notice the coefficients of x and y are related by convenient factors, so we can use the "elimination method" to solve these equations. Subtracting the first from the second, we get ...
(x +3y -5) -(x -15y -7) = 0 -0
18y +2 = 0 . . . . . . collect terms
y +1/9 = 0 . . . . . . . divide by 18, reduce the fraction
y = -1/9
Using this in the second equation, we have ...
x +3(-1/9) -5 = 0
x = 5 1/3
The solution to the system of equations is (x, y) = (5 1/3, -1/9).
