Find the point of intersection of the lines 3x+2y=15and7x-3y=4
To find the point of intersection of two lines, you need to solve the system of equations formed by the two lines. In this case, the system of equations is:
1) 3x + 2y = 15
2) 7x - 3y = 4
There are multiple methods to solve this system, but we will use the method of substitution. Here's how to find the point of intersection:
Step 1: Solve one equation for one variable in terms of one other variable. Let's solve equation 1) for x:
3x = 15 - 2y
x = (15 - 2y) / 3
Step 2: Substitute the value of x obtained in step 1 into the other equation (equation 2):
7((15 - 2y) / 3) - 3y = 4
Step 3: Simplify and solve for y:
(105 - 14y) / 3 - 3y = 4
(105 - 14y) - 9y = 12
105 - 14y - 9y = 12
105 - 23y = 12
- 23y = 12 - 105
- 23y = -93
y = (-93) / (-23)
y = 4
Step 4: Substitute the value of y back into equation 1) to find the corresponding x-value:
3x + 2(4) = 15
3x + 8 = 15
3x = 15 - 8
3x = 7
x = 7 / 3
So, the point of intersection of the lines 3x + 2y = 15 and 7x - 3y = 4 is (7/3, 4).