2x – y = 2 –x + 5y = 3 A. 0 B. 1 C. 2 D. infinitely many

How many solutions are there to the following system of equations? 2x

2 x - 1 y = 2

-2x + 10y = 6
-----------------add
9 y = 8
y = 8/9
etc
one solution

thanks

(19,_16,(_7,15)

To determine how many solutions there are to the system of equations, we can use the method of solving equations called elimination or substitution. Let's use the elimination method.

First, we need to eliminate one variable. Let's eliminate x. To do this, we multiply the first equation by -1 and add it to the second equation. The resulting equation will only contain the variable y.

The first equation becomes: -2x + y = -2
The second equation remains the same: -x + 5y = 3

Now we can add the two equations:
(-2x + y) + (-x + 5y) = (-2) + 3
Simplifying this equation, we get:
-3x + 6y = 1

Now we have a new equation:
-3x + 6y = 1

To solve for y, we can divide the whole equation by 3, so we get:
-3/3x + 6/3y = 1/3
Simplifying further:
-x + 2y = 1/3

Now we have a new equation:
-x + 2y = 1/3

At this point, we have eliminated x, and we are left with the equation -x + 2y = 1/3. This equation is linear and contains only one variable, y. Therefore, we can solve it to find the value of y.

To solve for y, we can multiply the equation by 3 to eliminate the fraction, which gives us:
-3x + 6y = 1

Now we can compare this equation with the previous one we obtained after elimination:
-3x + 6y =1
-3x + 6y = 1/3

By comparing the two equations, we see that they are equivalent. This means that both equations represent the same line, and we have infinitely many solutions. Therefore, the answer to the question is D. infinitely many.

In summary, by applying the elimination method and solving the system of equations, we found that there are infinitely many solutions to the given system of equations.