Question

(08.02 MC)A system of equations is shown below:y = 2x - 1y = 4x - 5Part A: Identify the slope and y-intercept for each equation. In your own words, explain how you cansolve the pair of equations by graphing. (8 points)Part B: Graph the two equation on the attached graph paper. What is the solution to the pair ofequations written in (x, y) form? (5 points)

Answer 1

Solving part A.

Step 1. The two equations we have are:

`\begin{gathered} y=2x-1 \\ y=4x-5 \end{gathered}`

To find the slope and y-intercept, we need to compare each equation with the slope-intercept equation:

`y=mx+b`

where m is the slope and b is the y-intercept of the line.

Step 2. Finding the slope and y-intercept of the two equations.

For the first equation, when we compare it with the slope-intercept equation we find that the values for the slope ''m'' and the y-intercept ''b'' are:

`\begin{gathered} m=2 \\ b=-1 \end{gathered}`

Doing the same for the second equation:

`\begin{gathered} m=4 \\ b=-5 \end{gathered}`

Step 3. explain how you can solve the pair of equations by graphing.

To solve the system by the graphing method we will need to make a graph that contains the two lines representing the two equations we have, and the point where those two lines intersect is the solution (x,y) of the system of equations.

Solving part B.

Step 4. In this part, we graph two lines, one with a slope of 2 that crosses the y-axis at -1, and the other with a slope of 4 that crosses the y-axis at -5.

The two lines are graphed in the following diagram:

The red line represents y=2x-1

and the blue line represents y=4x-5

The point where the lines meet is (2,3), this is the solution (x,y) to the pair of equations.

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Answer:

• Part A.

For the first equation:

slope = 2

y-intercep=-1

for the second equation:

slope=4

y-intercept=-5

Explanation to solve the equations by graphing:

To solve the system by the graphing method we will need to make a graph that contains the two lines representing the two equations we have, and the point where those two lines intersect is the solution (x,y) of the system of equations.

• Part B.

Graph:

The solution to the pair of equations:

(2,3)