The graph represents this system of equations. A system of equations. y equals 4 minus x. y equals y minus 2. A coordinate grid with 2 lines. The first line passes through (0, 4…

Question

asked Dec 27, 2021 67.5k views

2 Answers

Matthew H · Answer 1 · 2021-12-31T17:10:11+0000

Answer:

(3,1) is the correct answer.

Explanation:

It is given that first line passes through (0,4) and (3,1)

Let the two points be at coordinates:

(x_1,y_1) and
(x_2,y_2)

$x_1=0,\\y_1= 4,\\x_2=3,\\y_2= 1$

Equation of a line using two coordinates is given as:

y = mx+c

m = (y_2-y_1)/(x_2-x_1) = (1-4)/(3-0) = (-3)/(3) =-1

Put x = 0, y = 4

$4 = 0 +c\\\Rightarrow c = 4$

So, first equation is:
y = -x +4 ...... (1)

It is given that second line passes through (0,-2) and (3,1)

Let the two points be at coordinates:

(x_1,y_1) and
(x_2,y_2)

$x_1=0,\\y_1= -2,\\x_2=3,\\y_2= 1$

Equation of a line using two coordinates is given as:

y = mx+c

m = (y_2-y_1)/(x_2-x_1) = (1-(-2))/(3-0) = (3)/(3) =1

Put x = 0, y = -2

$-2 = 0 +c\\\Rightarrow c = -2$

So, second equation is:
y = x -2 ...... (2)

Solving equations (1) and (2) using substitution:

Adding Equation (1) and (2):

$2y = 4-2\\\Rightarrow y =1$

Putting value y = 1 in equation (1):

$1 = -x+4\\\Rightarrow x =3$

So, the solution for the system of equations is: (3,1)