Question

4x + 5y = 1,5, 8 x + 10 y = 3;​

Answer 1

$4x + 5y = 1.5 \\ 4x + 5y \times 0 = 1.5 \\ 4x + 0 = 1.5 \\ 4x = 1.5 \\ x = 0.375$

$8x + 5y = 1.5 \\ 8x + 10 \times 0 = 3 \\ 8x + 0 = 3 \\ 8x = 3 \\ x = \frac{3}{8}$

Answer 2

To solve the system of linear equations:

1. 4x + 5y = 1.5
2. 8x + 10y = 3

You can use the method of substitution or elimination. I'll use the elimination method in this example:

First, multiply the first equation by 2 to make the coefficients of y in both equations equal:

1. 8x + 10y = 3
2. 8x + 10y = 3

Now, subtract the second equation from the first equation to eliminate the variable x:

(8x + 10y) - (8x + 10y) = 3 - 3

This simplifies to:

0 = 0

This means that the two equations represent the same line in the xy-plane, and there are infinitely many solutions. In other words, the two equations are dependent, and the solution space is a straight line.

You can choose any value for x or y and solve for the other variable. For example, if we choose x = 0, we can solve for y in the first equation:

4x + 5y = 1.5 4(0) + 5y = 1.5 5y = 1.5 y = 1.5 / 5 y = 0.3

So, one possible solution is (x = 0, y = 0.3). However, there are infinitely many solutions along the line formed by these two equations.