5x+8y=-1 and 3x+y=7

Question

Explain how to solve a system of equations using the addition method.
Use 5𝑥 + 8𝑦 = −1 and 3𝑥 + 𝑦 = 7 to illustrate your explanation

 

Answer 1

5x + 8y = -1     ............ eq 1
3x + y = 7        ............. eq 2

 

multiply eq 2 with  -8 and then add eq 1 and eq 2

 

-24x - 8y =-56

 

5x +  8y = -1

_________________

-19x = -57

x = 3

 

subsitute x=3 in original eq 2

 

3(3) + y= 7

 9+y =7

y =-2

Answer 2

5x + 8y = -1

3x + y = 7

 

This might actually be an example of a system easier to solve by the substitution method, but in the elimination method requested, multiply the second equation by -8 and add the two equations.

 

-24x - 8y = 7

 

 

-19x = -57 and division by -19 give x = 3

 

then 9 + y = 7 => y = -2

 

You should now take these 2 answers and plug into the first equation to make sure it is correct.