Question

Which graph Represents the solution to the given system y=-x+5 y=1/4x+10

Answer 1

Shown below

Explanation:

In this exercise, we have the following system of linear equations in two variables:

$\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y=-x+5\\y=\frac{1}{4}x+10\end{array}\right.$

From the first equation:

$y=-x+5 \\ \\ \\ Slope \ m=-1 \\ \\ y-intercept \ b=5$

Here as x increases one unit, then y decreases by one unit too. Therefore, if (0, 5) is a point on the line, then (1, 4) is also a point on the line. From here, we know that the line must pass through these two points.

From the second equation:

$y=\frac{1}{4}x+10 \\ \\ \\ Slope \ m=\frac{1}{4} \\ \\ y-intercept \ b=10$

Here as x increases 4 units, then y increases by one unit Therefore, if (0, 10) is a point on the line, then (4,11) is also a point on the line. From here, we know that the line must pass through these two points.

By using graphing tool, we realize that both graphs intersect at a single point, which is:

$(-4, 9)$

The graph is shown below.

Learn more:

System of linear equations: https://brainly.com/question/13799715

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