- 3x + 7y = 1200 6x + 4y = 3500
what are the x and y values where the two lines intersect
To find the values of x and y where the two lines intersect, we can solve the system of equations using the method of substitution or elimination. Here, let's solve it using the method of elimination:
Given the system of equations:
1) 3x + 7y = 1200
2) 6x + 4y = 3500
First, we need to eliminate one variable by manipulating the equations. To eliminate the y variable, we'll multiply equation 1 by 4 and equation 2 by 7:
3) 12x + 28y = 4800
4) 42x + 28y = 24500
Now, subtract equation 3 from equation 4 to eliminate the y variable:
(42x + 28y) - (12x + 28y) = 24500 - 4800
Simplifying the equation:
30x = 19700
Dividing both sides of the equation by 30, we get:
x = 19700 / 30
x ≈ 656.67
Now, substitute the value of x back into either of the original equations (let's use equation 1):
3(656.67) + 7y = 1200
Simplifying the equation:
1970 + 7y = 1200
Subtracting 1970 from both sides:
7y = -770
Dividing both sides by 7, we get:
y = -770 / 7
y ≈ -110
Therefore, the lines intersect at approximately (x, y) ≈ (656.67, -110).