Question

What is the solution to the system of equations? Y=1/3x-10 2x+y=4

Answer 1

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)

Answer 2

Y = 1/3 x - 10 . . . (1)
2x + y = 4 . . . . . . (2)

Putting (1) into (2) gives, 2x + 1/3 x - 10 = 4
7/3 x - 10 = 4
7/3 x = 4 + 10 = 14
x = (3 x 14)/7 = 6

From (1), y = 1/3(6) - 10 = 2 - 10 = -8

x = 6, y = -8