Question

3) 4(3x + y) - 1 = y - 2x,2(4x - y) +19 = -x​

Answer 1

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Answer 2

To solve this system of linear equations:

1. 4(3x + y) - 1 = y - 2x
2. 2(4x - y) + 19 = -x

We can use the method of substitution or elimination. Let's use the elimination method:

First, simplify both equations:

1. 12x + 4y - 1 = y - 2x
2. 8x - 2y + 19 = -x

Now, let's get all the terms involving x and y on one side and the constants on the other side:

1. 12x + 4y + 2x - y = 1
2. 8x + x - 2y = -19

Combine like terms:

1. 14x + 3y = 1
2. 9x - 2y = -19

Now, we have a system of two linear equations:

1. 14x + 3y = 1
2. 9x - 2y = -19

Let's use the elimination method to solve this system. We can eliminate one variable by adding or subtracting the equations. In this case, let's eliminate y by multiplying the second equation by 3 and then adding the equations:

First, multiply the second equation by 3:

2. 3(9x - 2y) = 3(-19) 27x - 6y = -57

Now, add this modified equation to the first equation:

1. (14x + 3y) + (27x - 6y) = 1 - 57

Combine like terms:

41x = -56

Now, divide by 41 to solve for x:

x = -56 / 41

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

14x + 3y = 1 14(-56/41) + 3y = 1

Now, calculate:

-56(14/41) + 3y = 1

y = (1 + 56(14/41)) / 3

Now, calculate y:

y ≈ 2.438

So, the solution to the system of equations is approximately:

x ≈ -1.365 y ≈ 2.438