Questions: 2x + y = 5 y = mx + b y = -2x + 5 -2x + y = 1

2x + y = 5 y = mx + b y = -2x + 5 -2x + y = 1
Transcript text: 2x + y = 5 y = mx + b y = -2x + 5 -2x + y = 1
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Solution

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Solution Steps

Step 1: Rewrite the first equation in slope-intercept form.

The first system of equations is:

2x + y = 5 -2x + y = 1

To rewrite the first equation in slope-intercept form, isolate _y_:

2x + y = 5 y = -2x + 5

Step 2: Rewrite the second equation in slope-intercept form.

To rewrite the second equation in slope-intercept form, isolate _y_:

-2x + y = 1 y = 2x + 1

Step 3: Identify the solution to the system of equations.

The graphed solution shows the intersection point of the two lines is at (0,5) and (1,1). Also, adding the original two equations:

2x + y = 5 -2x + y = 1

2y = 6 y = 3

Substituting y=3 into the first original equation:

2x + 3 = 5 2x = 2 x = 1

Thus, the solution to this first system is (1,3). This also matches the circled solution on the page.

Step 4: Rewrite the second equation from the image.

The second set of equations is:

y=mx+b -2x+y=1

Rewriting the second equation:

y=2x+1

Step 5: Identify the solution to the second system of equations.

The solution to this system of equations is y = 2x + 1. The points (0,1) and (1,-1) are circled and are incorrect. The line y=2x+1 passes through the points (0,1), (1,3), and (2,5), as shown on the graph.

Final Answer

The solution to the first system of equations 2x + y = 5 and -2x + y = 1 is (1,3). The second system of equations y = mx + b and -2x + y = 1 represents the linear equation y=2x + 1, containing points such as (0,1), (1,3) and (2,5).

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