Answer:
The solution for the given system of equation is: (21, -3)
Step-by-step explanation:
Given the system of equation:
[tex]y = \frac{1}{3}x -10[/tex] .....[1]
[tex]2x+y = 4[/tex] .....[2]
We can write [2] as:
[tex]y = 4-2x[/tex] ......[3]
Equate [2] and [3] we have;
[tex]4-2x=\frac{1}{3}x-10[/tex]
add 10 to both sides we get;
[tex]14-2x=\frac{1}{3}x[/tex]
Add 2x to both sides we get;
[tex]14=\frac{1}{3}x+2x[/tex]
Combine like terms;
[tex]14 = \frac{7}{3}x[/tex]
Divide both sides by 7 we get;
[tex]2 = \frac{x}{3}[/tex]
Multiply both sides by 3 we get;
[tex]6=x[/tex]
or
x =6
Substitute the value of x in [1] we have;
[tex]y = \frac{1}{3}(6) -10[/tex]
⇒[tex]y = 2-10= -8[/tex]
Therefore, the solution for the given system of equation is: (6, -8)
