Find the point of intersection:
y=3x+y
y=-2x+9
My work:
3x+4= -2x+9
3x+4-4=-2x+9-4
continued because I accidentally hit submit
3x=-2x+5
3x+2x=-2x+5+2x
5x=5
x=1
Is my answer correct? Do I need to add anything?
so what is y?
I think you mean
Find the point of intersection:
y=3x+4
y=-2x+9
Now if x = 1
y = 3*1 + 4 = 3+4 = 7
now check with second equation
y = -2(1) + 9 = 9-2 = 7 CARAMBA!!!
To find the point of intersection between the two given lines, you need to solve the system of equations. Let's start by simplifying the equations:
Equation 1: y = 3x + y
This equation doesn't provide any new information since it states that y is equal to itself (y = y). Therefore, we can ignore this equation when solving the system.
Equation 2: y = -2x + 9
Now we can substitute this equation into the first equation to eliminate y:
-2x + 9 = 3x + y
Next, we'll rearrange the equation to isolate one variable:
-2x - 3x = y - 9
-5x = y - 9
Now, we can substitute this expression for y back into either of the original equations. Let's use Equation 2:
y = -2x + 9
-5x = -2x + 9 - 9
-5x = -2x
-5x + 2x = 0
-3x = 0
x = 0
Once we have the value of x, we can substitute it back into any of the original equations to find the value of y. Let's use Equation 2 again:
y = -2(0) + 9
y = 9
Therefore, the point of intersection between the two lines is (0, 9).