Question

Graph the system below and write its solution.2x+y=6Note that you can also answer "No solution" or "Infinitely many" solutions.10. 8 6jaf18-6m44-2444fon10Solution:

Answer 1

• Solution: (4, -2)

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• Graph: ,first equation in red and second equation in purple. Solution in orange.

Step-by-step explanation

The two equations in the system are linear equations, so their graphs are lines. The solution to the system is the point where the two lines intersect.

The first equation is in the slope-intercept form. The y-intercept is -1, and we can find the x-intercept by substituting y = 0,

`0=-(1)/(4)x-1`

Solving for x,

`x=4\cdot(-1)=-4`

So, the line passes through the points (0, -1) and (-4, 0),

The second equation is in standard form. We can find the x and y-intercepts by substituting y and x with 0, respectively,

`\begin{gathered} 2\cdot0+y=6 \\ \\ y=6 \end{gathered}`
`2x+0=6\Rightarrow x=(6)/(2)=3`

Thus, the y-intercept is (0, 6) and the x-intercept is (3, 0),

And the point where the two lines intersect is the solution,

Hence, the solution is (4, -2).