Question

Find the general solution of the following system of equations.
{−7x−2y=-4, −21x−6y=−12

Answer 1

To find the general solution of the system of equations, we can solve one equation for one variable and substitute that expression into the other equation.

Step-by-step explanation:

To find the general solution of the system of equations, we can solve one equation for one variable and substitute that expression into the other equation. Let's solve the first equation for x:

-7x - 2y = -4

x = (2y - 4) / -7

Now substitute this expression for x in the second equation:

-21x - 6y = -12

-21((2y - 4) / -7) - 6y = -12

Simplify the equation:

6y = -12

y = -2

Substitute this value of y back into the expression for x:

x = (2(-2) - 4) / -7

x = 0

Therefore, the general solution of the system of equations is x = 0 and y = -2.

Answer 2

x = x (parameter),

y = (4 - 7x)/2.

Step-by-step explanation:

To find the general solution of the system of equations:

{-7x - 2y = -4,

-21x - 6y = -12},

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

We can multiply the first equation by 3 to make the coefficients of x in both equations equal:

{3(-7x - 2y) = 3(-4),

-21x - 6y = -12}.

Simplifying, we get:

{-21x - 6y = -12,

-21x - 6y = -12}.

Since both equations are identical, we have infinitely many solutions. We can express the general solution in terms of a parameter. Let's solve for y:

-21x - 6y = -12.

Dividing by -3, we get:

7x + 2y = 4.

Rearranging the equation to solve for y, we have:

2y = 4 - 7x,

y = (4 - 7x)/2.

Therefore, the general solution for the system of equations is:

x = x (parameter),

y = (4 - 7x)/2.