Respuesta :
EXPLANATION
Suppose that we have the following system of equations:
(1) x + 2y = 30
(2) 3x + y = 14
The key is to isolate one variable from one equation and substitute into another in order to get the first solution:
We can first isolate x from (1) by subtracting -2y to both sides:
x + 2y - 2y = 30 - 2y
Simplifying:
x = 30 - 2y
Plugging in x = 30 - 2y into the second equation:
[tex]3(30-2y)+y=14[/tex]Applying the distributive property:
[tex]90-6y+y=14[/tex]Adding like terms:
[tex]90-5y=14[/tex]Subtracting -90 to both sides:
[tex]-5y\text{ = 14 - 90}[/tex]Dividing both sides by -5:
[tex]y=\frac{14-90}{-5}[/tex]Subtracting numbers:
[tex]y=\frac{-76}{-5}[/tex]Simplifying:
[tex]y=\frac{76}{5}[/tex]Now, plugging in y=76/5 into the first equation:
[tex]x+2\cdot\frac{76}{5}=30[/tex]Multiplying numbers:
[tex]x+\frac{152}{5}=30[/tex]Subtracting -152/5 to both sides:
[tex]x=30-\frac{152}{5}[/tex]Subtracting numbers:
[tex]x=-\frac{2}{5}[/tex]In conclusio, the solution to the system of equation is:
x=-2/5, y=76/5
