Respuesta :
Answer:
[tex]x=5\ and\ y=-8[/tex]
The solution of the system can be given as (5,-8).
Step-by-step explanation:
Given system of equations:
[tex]y=-x-3[/tex]
[tex]5x+2y=9[/tex]
To solve the given system of equations:
Solution:
We will use substitution to solve the given system.
We will substitute the [tex]y[/tex] values in terms of [tex]x[/tex] from the equation [tex]y=-x-3[/tex] into the other equation to solve for [tex]x[/tex]
Substituting [tex]y=-x-3[/tex] into [tex]5x+2y=9[/tex].
We have:
[tex]5x+2(-x-3)=9[/tex]
Using distribution.
[tex]5x-2x-6=9[/tex]
Combining like terms.
[tex]3x-6=9[/tex]
Adding 6 both sides.
[tex]3x-6+6=9+6[/tex]
[tex]3x=15[/tex]
Dividing both sides by 3.
[tex]\frac{3x}{3}=\frac{15}{3}[/tex]
∴ [tex]x=5[/tex]
Plugging in [tex]x=5[/tex] into [tex]y=-x-3[/tex].
We have,
[tex]y=-5-3[/tex]
∴ [tex]y=-8[/tex]
The solution of the system can be given as (5,-8).
