The solution to the linear system is x = 22 and y = 16.
To solve the given linear system, we can use the method of substitution or elimination. Let's use the elimination method in this case. The first step is to eliminate one variable by adding or subtracting the two equations. To do that, we need to manipulate the equations to make the coefficients of one variable opposites of each other.
By multiplying the first equation by 2 and the second equation by 5, we can make the coefficients of y in both equations opposites:
1) 0.4x - y = -7.6
2) 1.5x + 2y = 52
Now, by adding these two equations, we can eliminate y:
1.9x = 44.4
x = 44.4 / 1.9
x = 22
Next, we substitute the value of x back into one of the original equations to solve for y:
0.2(22) - 0.5y = -3.8
4.4 - 0.5y = -3.8
-0.5y = -8.2
y = -8.2 / -0.5
y = 16
Thus, the solution to the linear system is x = 22 and y = 16.
Step-by-step explanation:
In this problem, we were given a system of two linear equations with two variables, x and y. To find the solution, we employed the elimination method, which involves eliminating one variable by adding or subtracting the equations in a way that the coefficients of the variable become opposites. By carefully manipulating the equations and adding them, we successfully eliminated y and solved for x. Substituting the value of x back into one of the original equations allowed us to find the value of y.
Linear systems are essential in various fields, including mathematics, engineering, physics, and economics. They represent a set of equations that can be used to model real-world situations and make predictions. Solving these systems helps in finding the intersection points of multiple lines, which hold significant meaning in different contexts.