What is the point of intersection of the lines 16x+14y=-8 and 4x+18y+2=0 ?
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We can find the solution to this system of equations by the elimination method.
Step 1: Subtract 2 from both sides of 4x + 18y +2 = 0
The equation becomes 4x + 18y = -2
Step 2: Multiply all terms in the equation 4x + 18y = -2 by -4
The equation becomes -16x -72y = 8
Step 3: Writing...
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The intercepting point of the lines could be determined by solving the system. We'll use the substitution method to determine the solution of the system.
We'll divide the first equation by 2:
8x + 7y = -4 (1)
We'll divide the 2nd equation by 2:
2x + 9y + 1 = 0
We'll subtract 1 both sides:
2x + 9y = -1 (2)
In (2), we'll subtract 9y both sides:
2x = -1 - 9y
We'll divide by 2:
x = -(1+9y)/2 (3)
We'll substitute (3) in (1):
-8(1+9y)/2+7y = -4
We'll simplify:
-4(1+9y) + 7y = -4
We'll remove the brackets:
-4 - 36y + 7y = - 4
We'll combine like terms:
-4 - 29y = -4
We'll eliminate like terms:
-29y = 0
y = 0
We'll substitute y in x:
x = -(1+9*0)/2
x = -1/2
The solution of the system represents the coordinates of the intercepting point of the lines: {(-1/2 , 0)}.
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