Question

what is the solution to the system of equations? y =1/3 x – 10 2x y = 4 (–8, 6) (–6, 16) (6, –8) (16, –6)

Answer 1

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:

Answer 2

Y = 1/3 x - 10
2x + y = 4
2x + 1/3 x - 10 = 4
7/3 x = 14
x = 6
y = 1/3(6) - 10 = 2 - 10 = -8
Therefore solution is (6, -8)