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

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