Question

Solve the system of two linear equations. -3x-4y=-23. 3x-5y=5

Answer 1

To solve the system of linear equations, we can use the method of elimination.

First, we multiply the second equation by 2 to make the x-coefficients cancel out when added to the first equation:

2 * (3x - 5y) = 2 * 5
6x - 10y = 10

Next, we add the modified second equation to the first equation:

(-3x - 4y) + (6x - 10y) = -23 + 10
3x - 14y = -13

Now, we have a new equation:

3x - 14y = -13

To eliminate the y-term, we can multiply the first equation by 14 and the second equation by -4:

14 * (-3x - 4y) = 14 * (-23)
-42x - 56y = -322

-4 * (3x - 5y) = -4 * 5
-12x + 20y = -20

Adding these two modified equations together:

(-42x - 56y) + (-12x + 20y) = -322 - 20
-54x - 36y = -342

Now, we have another new equation:

-54x - 36y = -342

To eliminate the x-term, we can multiply the first equation by 36 and the second equation by -14:

36 * (3x - 14y) = 36 * (-13)
108x - 504y = -468

-14 * (-54x - 36y) = -14 * (-342)
756x + 504y = 4788

Adding these two modified equations together:

(108x - 504y) + (756x + 504y) = -468 + 4788
864x = 4320

Dividing both sides by 864:

x = 5

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

-3x - 4y = -23
-3(5) - 4y = -23
-15 - 4y = -23
-4y = -23 + 15
-4y = -8
y = -8 / -4
y = 2

So the solution to the system of linear equations is x = 5 and y = 2.