Question

How many solutions does the system of equations have? y=-2x+9 6x + 3y =27(1 point)

Answer 1

To find the number of solutions for this system of equations, we can solve it using the elimination method or substitution method.

First, let's solve the first equation y = -2x + 9 for x in terms of y by rearranging it:

2x + y = 9,
2x = 9 - y,
x = (9 - y)/2.

Now, substitute this expression for x in the second equation:

6x + 3y = 27,
6((9 - y)/2) + 3y = 27,
3(9 - y) + 3y = 27,
27 - 3y + 3y = 27,
27 = 27.

Since we obtained a true statement at the end (27 = 27), this system of equations has infinitely many solutions.