What is the graph of the system y = -2x + 3 and 2x + 4y = 8?

Solution:

It is given that

y = - 2x + 3 …. (1)

2x + 4y = 8 …. (2)

Substituting equation (1) in (2)

2x + 4 (-2x + 3) = 8

Using the multiplicative distributive property

2x - 8x + 12 = 8

On rearranging

2x - 8x = 8 - 12

-6x = - 4

Dividing both sides by -2

3x = 2

x = 2/3

Substituting the value of x in equation (1)

y = -2 (2/3) + 3

y = -4/3 + 3

Taking LCM

y = (-4 + 9)/3

y = 5/3

Therefore, the graph of the system is (2/3, 5/3).

What is the graph of the system y = -2x + 3 and 2x + 4y = 8?

Summary:

The graph of the system y = -2x + 3 and 2x + 4y = 8 is (2/3, 5/3).