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