Use addition or substitution to find the value of x for this set of equations.

Solving Systems of Linear Equations

2 Ways.

1. Substitution

2. Linear Combination/ Elimination Method

Problem:

1. 4x + 13y = 40

2. 4x + 3y= -40

USING. Linear Combination/ Elimination Method

STEPS

1. Label each equation with number 1- however many there are

2. Choose a VARIABLE to cancel when you ADD the linear equations

(easiest one...ex. Whole number if possible)

3. Multiply one of the equations by the opposite(-1 in this case) 1. 4x + 13y = 40

2. (-1)( 4x + 3y) =( -40)(-1)

or whatever number will cancel the variable

4. Add both equations together to cancel one of the variables ( x in this case).

5. Solve for other variable(y in this case). 1. 4x + 13y = 40

2. - 4x +- 3y = 40

10y=80

y=8

6. Plug in value for solved variable into one of the ORIGINAL equations. y=8. 1. 4x + 13y = 40

1. 4x + 13(8)= 40

1. 4x +104= 40

4x=40+-104=-64

x=-64/4=-16

7. Check solution for x and y in both original equations by plugging in your answers to x and y to see if the equations are true(equal on both side)

x=-16, y=8. Substitute into Equation 2. 4x + 3y= -40

-64 + 24=-40 Check

Therefore, these lines intersect at point ( -16, 8).

NOTE: If the point would not have checked then here are the possible solutions to linear equations regardless of how you solve them.

POSSIBLE SOLUTIONS

1. There is a solution that makes both equations true so they INTERSECT at that point. Solution is the point that is a solution for all linear equations (x,y).

2. There is NOT a solution to the equations they DO NOT INTERSECT And are PARALLEL. Solution is { }

3. All real numbers make both equations true so they are COINCIDENT LINES aka the same line. Solution is all real numbers or which ever number family you are working with.

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