The solution of the system of linear equations is (x, y) = (9, 1).
How to solve on a system of linear equations
In this situation we have the case of a system formed by two linear equations, each of the with two variables. There are several methods of solution, a graphic ones and several algebraic ones. In this case we shall use the determinant method, which offers an agile though efficient method of solution.
First, we organize the system in standard form:
- 2 · x + 3 · y = - 15
x + y = 10
Second, we determine the determinant of the matrix of dependent coefficients:
[tex]D = \left|\begin{array}{cc}- 2&3\\1&1\end{array}\right|[/tex]
D = (- 2) · 1 - 1 · 3
D = - 5
Third, we determine the determinants associated with each variable:
[tex]D_{1} = \left|\begin{array}{cc}- 15&3\\10&1\end{array}\right|[/tex]
D₁ = - 15 · 1 - 10 · 3
D₁ = - 15 - 30
D₁ = - 45
[tex]D_{2} = \left|\begin{array}{cc}- 2&- 15\\1&10\end{array}\right|[/tex]
D₂ = (- 2) · 10 - 1 · (- 15)
D₂ = - 5
Finally, we determine the solution of the entire system:
x = D₁ / D
x = (- 45) / (- 5)
x = 9
y = D₂ / D
y = (- 5) / (- 5)
y = 1
The solution of the system of linear equations is (x, y) = (9, 1).
To learn more on systems of linear equations: https://brainly.com/question/20379472
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