Question

Which graph shows the solution to the system of linear equations? y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2

Answer 1

a line

Explanation:

y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2

Answer 2

B) A coordinate plane with one line that passes through the points (0, 4) and (2, 3) and another line that passes through the points (0, 0) and (2, 1)

Explanation:

Given system of linear equations:

`\begin{cases}y=(1)/(2)x\\x+2y=8\end{cases}`

Substitute the first equation into the second equation and solve for x:

`\implies x+2\left((1)/(2)x\right)=8`

`\implies x+x=8`

`\implies 2x=8`

`\implies x=4`

Substitute the found value of x into the first equation and solve for y:

`\implies y=(1)/(2)(4)`

`\implies y=2`

Therefore, the solution to the given system of linear equations is:

• (4, 2)

The point of intersection is the solution to a graphed system of linear equations.

Therefore, the graph that shows the solution to the given system of linear equations is the graph where the point of intersection of the two lines is (4, 2).