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# 4x + 13y = 40 4x + 3y = -40

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

### 4 Answers by Expert Tutors

Rachel N. | Awesome Math Tutoring: Make Math Fun Again!Awesome Math Tutoring: Make Math Fun Aga...
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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.

Jon G. | Patient knowledgeable STEM educator/former healthcare practitionerPatient knowledgeable STEM educator/form...
4.9 4.9 (7 lesson ratings) (7)
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Stephen H. | Tutor of Math, Physics and Engineering ... available onlineTutor of Math, Physics and Engineering ....
4.8 4.8 (281 lesson ratings) (281)
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Use a step by step approach and it helps to number the lines. 1) Given:4x + 13y = 40 2) Given:4x + 3y = -40 3) Modify one of the equations to express one of the variables (x or y) in terms of the other. Line 1) can be re-arranged to the form below. 4) x=10-13/4y 5) Substitute the expression for x into line 2) resulting in the below. 6) 40-13y+3y=-40 7) Solve 6) for y 8) Simplify by subtracting 40 from both sides 9) -13y+3y=-40-40=-80 10) combine the left side into -10y 11) -10y=-80 12)divide both sides by -10 13) y=8 14) substitute 8 for y in either 1) or 2). 15) Choosing 1) 4x + 13(8)=40 16) Solving for x results in that x=-64/4=-16 Summary is that each equation has the same result when x=-16 & y=8.
Kurt T. | Math Tutoring and Test PrepMath Tutoring and Test Prep
4.9 4.9 (124 lesson ratings) (124)
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We need to eliminate one of the variables.  Here, the easiest way to do it is to subtract one equation from the other.

(4x + 13y = 40) - (4x + 3y = -40) = (10y = 80).  The x term drops out.

10y = 80, so y = 8,  Now substitute 8 for y in both equations and confirm that both produce the same value for x.

4x + (13 * 8) = 40

4x + 104 = 40

4x = -64

x = -16

4x + (3 * 8) = -40

4x + 24 = -40

4x = -64

x = -16