Question

a system of equations and its graph are shown.
y=3x + 2
y= - 2x - 3
which is the solution to the system?

Answer 1

To find the solution to the system of equations, we need to find the point where the two equations intersect, since that is where the values of x and y satisfy both equations simultaneously.

To find the intersection point, we can set the two equations equal to each other:

3x + 2 = -2x - 3

Adding 2x to both sides gives: 5x + 2 = -3

Subtracting 2 from both sides gives: 5x = -5

Dividing both sides by 5 gives: x = -1

Now, we can substitute this value of x back into one of the equations to find the corresponding value of y:

Using the first equation y = 3x + 2, when x = -1:

y = 3(-1) + 2

y = -3 + 2

y = -1

So, the solution to the system is x = -1 and y = -1.

The graph of the system will show two lines intersecting at the point (-1, -1).