Determine the number of solutions to this system of lineer equations
2x+y=6
4x+2y=8
Answer choise
0
2
infinte
1
The given system of linear equations is:
2x + y = 6 ...(1)
4x + 2y = 8 ...(2)
We can simplify equation (2) by dividing both sides by 2:
2x + y = 4 ...(3)
Now, if we compare equations (1) and (3), we can see that they represent the same line. The two equations have the same slopes and y-intercepts.
This means that the two equations are dependent, and they represent the same line. Therefore, they have infinitely many solutions.
So, the correct answer is: infinite.
Determine the number of solutions to this system by insetcion and classify the syatem
3x+7y=8
4x+y=10
To determine the number of solutions to the system and classify it, we can solve the system using the method of substitution or elimination.
Let's solve the system using the method of elimination:
Multiply equation (2) by 7 to make the coefficients of y in both equations equal:
7(4x + y) = 7(10)
28x + 7y = 70 ...(3)
Now, we can subtract equation (1) from equation (3) to eliminate the variable x:
(28x + 7y) - (3x + 7y) = 70 - 8
28x - 3x + 7y - 7y = 62
Simplifying the equation, we get:
25x = 62
Solving for x, we find:
x = 62/25
Now, we can substitute the value of x back into either of the original equations to solve for y. Let's use equation (1):
3x + 7y = 8
3(62/25) + 7y = 8
186/25 + 7y = 8
7y = 8 - 186/25
7y = (200 - 186) / 25
7y = 14 / 25
y = 14 / (7 * 25)
y = 2 / 25
So, the solution to the system is:
x = 62/25
y = 2/25
Therefore, the system has 1 solution, and it is a consistent system because it has a unique solution.