[tex]x = 23[/tex]
Step-by-step explanation:
First, we need to write the equations in their standard form, i.e., all the variables and their coefficients are to be placed on the left hand side and the plain numbers on the right hand side. The first equation is already in its standard form:
[tex]2x + 5y = 35\;\;\;\;\;(1)[/tex]
but we need to rewrite the 2nd one. So the standard form of the 2nd equation can be written as
[tex]x + 15y = -10\;\;\;\;\;(2)[/tex]
Now that the equations are in their standard forms, the next step that we need to do is to eliminate one of the variables, namely the y. To do that, we need to multiply either one of the equations so that when we add them together, the y-variable gets eliminated. Note if we multiply Eqn(1) by -3, we'll get -15y on one equation and a +15y on the other equation so that when they are added together, they cancel out. So if we do that, we get
[tex]-6x - 15y = -105\;\;\;\;\;(3)[/tex]
Adding Eqn(3) to Eqn(2), we get
[tex]-5x = -115[/tex]
or
[tex]x = \dfrac{-115}{-5} = 23[/tex]
