Question

What is the solution to the following system of linear equations?

{4x - y = -6
{x - 2y = -5

Please explain how you solved!

Answer 1

The solution to the system of linear equations is x = -1, y = 2

Step-by-step explanation:

To solve the system of linear equations:
4x - y = -6
x - 2y = -5
We can use the method of substitution or elimination to find the solution.
Let's use the elimination method. We can multiply the second equation by 4 to make the coefficients of x in both equations the same.
4(x - 2y) = 4(-5)
4x - 8y = -20
Now, we can subtract the second equation from the first equation to eliminate x.
(4x - y) - (4x - 8y) = (-6) - (-20)
-y + 8y = 14
7y = 14
y = 2
Substituting y = 2 back into the first equation:
4x - 2 = -6
4x = -4
x = -1
The solution to the system of linear equations is x = -1, y = 2

Answer 2

There are two ways to solve system of equations.

1) substitution method

2) elimination method

4x - y = -6

x - 2y = -5

For thus problem, i'll be using the substitute method.

So, using the equation x - 2y = -5:

Solve for "x" by adding 2y to both sides of the equation.

x = 2y - 5

Now we know what "x" is, we can substitute it in the other equation.

4x - y = -6

4(2y - 5) - y = -6

8y - 20 - y = -6

7y - 20 = -6

7y = 14

y = 2

We now know the numerical value of y. So, all we have to do is plug in y into either system of equation to solve for the numerical value of x.

4x - 2 = -6 x - 2y = -5

4x = -4 x - 2(2) = -5

x = -1 x - 4 = -5

x = -1



The solution is (-1, 2) where x equals -1 and y equals 2.