Question

What is the solution to the system of equations graphed below

Answer 1

Answer:  The correct option is (D) (1, -2).

Step-by-step explanation:  We are given to find the solution to the following system of equations graphed in the picture :

$y=-4x+2~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Comparing equations (i) and (ii), we get

$-4x+2=x-3\\\\\Rightarrow 4x+x=2+3\\\\\Rightarrow 5x=5\\\\\Rightarrow x=\dfrac{5}{5}\\\\\Rightarrow x=1.$

Substituting the value of x in equation (ii), we get

$y=x-3=1-3=-2.$

Thus, the required solution of the given system is (x, y) = (1, -2).

Option (D) is CORRECT.

Answer 2

Equation 1 ==> y = -4x + 2
Equation 2 ==> y = x - 3

Substitude equation 2 into 1

x - 3 = -4x + 2
-5 = -5x
x = 1

Substitude x into equation 2

y = 1 - 3
y = -2

Coordinates is (1, -2)
Answer is D.