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