For this case we have a system of two linear equations with two unknowns. whose variables are given by x and y respectively.
To solve the system by the linear combination method we follow the following steps:
1st step:
We multiply the first equation by 5:
[tex]35x + 10y = 145[/tex]
2nd step:
We multiply the second equation by 2:
[tex]6x-10y = 60[/tex]
3rd step:
We add the equations:
[tex]35x + 10y = 145\\6x-10y = 60[/tex]
Thus, we obtain the following:
[tex]41x = 205[/tex]
[tex]x =\frac{205}{41}[/tex]
[tex]x = 5[/tex]
4th step:
We substitute [tex]x= 5[/tex] in any of the equations:
[tex]3 (5) -5y = 30\\15-5y = 30\\-5y = 30-15\\-5y = 15[/tex]
[tex]y =\frac{15}{-5}\\y = -3[/tex]
Thus, the values of the variables are[tex]x = 5[/tex]and [tex]y = -3[/tex].
Answer:
The values are: [tex]x = 5[/tex]and [tex]y = -3[/tex].
