Solve the following system using the substitution method:
6x - 2y = -4
y = 3x + 2
sub the 2nd into the 1st:
6x - 2(3x+2) = -4
6x - 6x - 4 = -4
-4 = -4
infinite number of solutions, just use the 2nd, pick any x you feel like, and get the y
e.g.
x = 2
y = 3(2)+2 = 8
etc
What you really have is the same equation twice.
(multiply the 2nd by 2 and you will get the 1st)
Which of the following solution of the given system of linear equations?
{x-2y=-16
{6x+2y=-26
To solve this system using the substitution method, we need to solve one equation for one variable and substitute it into the other equation.
Let's solve the second equation for y:
y = 3x + 2
Now, substitute this expression for y in the first equation:
6x - 2(3x + 2) = -4
Simplify the equation:
6x - 6x - 4 = -4
Combine like terms:
-4 = -4
This equation is already simplified, and we can see that the equation is true. This means that the system of equations is dependent, and the two equations represent the same line.
Therefore, there are infinitely many solutions to this system.
To solve this system using the substitution method, we need to substitute the value of y from the second equation into the first equation. Let's substitute y = 3x + 2 into the first equation:
6x - 2(3x + 2) = -4
Simplify the equation:
6x - 6x - 4 = -4
Since the x terms cancel each other out, we are left with:
-4 = -4
This equation is always true, which means that the system is dependent. In other words, the two equations represent the same line. This means that the system has infinitely many solutions, since any point on the line satisfies both equations.
Therefore, the solution to this system is all the points on the line y = 3x + 2.