Question

How many solutions does y=5-2x 4x+2y = 10

Answer 1

Infinitely Many

Explanation:

Equations:

y = 5 - 2x

4x + 2y = 10

There are multiple ways to solve this, but I'm going to use substitution.

Since y = 5 - 2x, I will input this y value into the second equation.

4x + 2(5 - 2x) = 10

From here, it's simple algebra.

4x + 10 - 4x = 10

- 10 - 10

4x - 4x = 0

0x = 0

Because we essentially have the solution 0 = 0, this means that the system has an infinite amount of solutions.

Why?

Well, they're the same line. (Put both into slope intercept form.)

y = 5 - 2x OR y = -2x + 5

4x + 2y = 10

2y = -4x +10

= y = -2x + 5

Answer 2

INFINITE SOLUTIONS.

Explanation:

y = 5 - 2x

4x + 2y = 10

From the first equation:

2x + y = 5 Multiply this equation by -2:

-4x - 2y = -10

Adding the above to the second equation:

0 = 0 So the 2 equations are identical and there are Infinite SOLUTIONS>