Answer:
Option C is correct.
Solution to the given system of equation is (6 , -8)
Step-by-step explanation:
Given the system of equation:
\(y= \frac{1}{3} x-10\) ......[1]
\(2x+y =4\) .....[2]
Substitute the equation [1] in [2] we get;
\(2x +\frac{1}{3}x -10 =4\)
Combine like terms;
\(\frac{7}{3}x -10 =4\)
Add 10 to both side of an equation:
\(\frac{7}{3}x -10 +10=4+10\)
Simplify:
\(\frac{7}{3}x =14\)
Divide both sides by \(\frac{3}{7}\) we get;
\(\frac{3}{7} \times \frac{7}{3}x = 14 \times \frac{3}{7}\)
Simplify:
x = 6
Substitute the value of x =6 in equation [1] we get;
\(y= \frac{1}{3}(6)-10\)
or
\(y= 2-10\)
Simplify:
y = - 8
therefore, the solution to the given system of equation is; (6 , -8)
You can also see in the graph as shown below:
