What is the point of intersection of the lines 16x+14y=-8 and 4x+18y+2=0 ?

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academicsfirst's profile pic

academicsfirst | High School Teacher | (Level 2) Adjunct Educator

Posted on

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 both equations in a vertical format, combine as follows:

16x + 14 y = -8

-16x  - 72y  = 8

0x  -  72y = 0

-72y =0

Dividing by -72,         y=0

Substitute 0 for y in the first equation  and solve for x as follows:

16x + 14y = -8

16x + 14(0) = -8

16x  + 0 = -8

16x = -8

Dividing by 16,           x = -1/2

Therefore our solution is  {(-1/2, 0)}

 

We can check our answers by substituting the values for x and y into both equations.

16x + 14y = -8

16(-1/2) + 14(0) = -8

-8 = -8

4x + 18y + 2 =0

4(-1/2) + 18(0) + 2 = 0

-2 +  0 + 2  = 0

0=0

Eliminating is my favorite part of solving equations!

 

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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