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How many solutions does this linear system have?
y=-3x+4
x + 2y = 8
O
O
O
O
one solution: (8,0)
one solution: (0,8)
no solution
infinite number of solutions

Respuesta :

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Answer:

x = 0 , y = 4

Step-by-step explanation:

Solve the following system:

{y = 4 - 3 x | (equation 1)

x + 2 y = 8 | (equation 2)

Express the system in standard form:

{3 x + y = 4 | (equation 1)

x + 2 y = 8 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x + y = 4 | (equation 1)

0 x+(5 y)/3 = 20/3 | (equation 2)

Multiply equation 2 by 3/5:

{3 x + y = 4 | (equation 1)

0 x+y = 4 | (equation 2)

Subtract equation 2 from equation 1:

{3 x+0 y = 0 | (equation 1)

0 x+y = 4 | (equation 2)

Divide equation 1 by 3:

{x+0 y = 0 | (equation 1)

0 x+y = 4 | (equation 2)

Collect results:

Answer: {x = 0 , y = 4

The correct option regarding the number of solutions of the system of equations is given by:

one solution: (0,4).

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the system is:

y = -3x + 4

x + 2y = 8

Replacing the first equation on the second:

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

x - 6x + 8 = 8

-5x = 0

x = 0

y = -3x + 4 = -3(0) + 4 = 4

Hence, the correct option is:

one solution: (0,4).

More can be learned about a system of equations at https://brainly.com/question/24342899

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