Question

Determine the number of solutions
2x+y=6
4x+2y=8

Answer 1

4x-8y=-36
-6x+y=32

What is the answer? (__,__)

Answer 2

No decimal

Answer 3

The two equations can be rewritten as:
y = 6 - 2x
y = 4 - 2x

Since the equations represent the same line, there are infinite solutions.

Answer 4

To find the solution to this system of equations, we can use the method of substitution or elimination. Let's use the elimination method:

Multiply the second equation by 8 to make the coefficients of y in both equations equal.

-6x + y = 32
64x - 8y = 256

Now we can subtract the modified second equation from the first equation to eliminate y:

4x - 8y = -36
-64x + 8y = -256
70x = -292
x = -292 / 70
x = -4.17

Now we substitute x back into one of the equations to solve for y:

4(-4.17) - 8y = -36
-16.68 - 8y = -36
-8y = -19.32
y = -19.32 / -8
y = 2.42

Therefore, the solution is (-4.17, 2.42).

Answer 5

Let's rewrite the equations with integer coefficients:

4x - 8y = -36
-6x + y = 32

Now, we can use the elimination method to solve this system of equations:

Multiplying the second equation by 8, we get:
-48x + 8y = 256

Adding the new equation to the first equation to eliminate y:
-44x = 220
x = -5

Substitute x back into the second equation to find y:
-6(-5) + y = 32
30 + y = 32
y = 2

Therefore, the solution to the system of equations is (-5, 2).