Question

2x-3y=-7
`y=2x+9`
How many solutions are there?
1
No Solution
Infinitely Many Solutions

Answer 1

To determine the number of solutions, we can solve the system of equations.

Firstly, we can rearrange the second equation to be in the form of y = mx + b:

y = 2x + 9

Now, we can substitute this expression for y in the first equation:

2x - 3(2x + 9) = -7

Simplifying the equation, we have:

2x - 6x - 27 = -7

Combining like terms:

-4x - 27 = -7

Adding 27 to both sides:

-4x = 20

Dividing by -4:

x = -5

Now, substitute this value of x back into either of the original equations to solve for y. Let's use the second equation:

y = 2(-5) + 9

y = -10 + 9

y = -1

So, the solution to the system of equations is (x, y) = (-5, -1).

Since there is a unique solution, there is exactly 1 solution to the system of equations.