Question

Solve the following system of linear equations by graphing.{5x - 2y = 10 {x - y = -1 Graph the equations on the same set of axes.Note: Use different points on each line when plotting the graphs.The solution point is: (_, _)

Answer 1

Kindly Check below

1) The first thing we need to do in this question, is to pick the method we are going to use to solve this system. Let's use the Elimination Method.

2) So, let's solve this system analytically (algebraically):

`\begin{gathered} 5x-2y=10 \\ x-y=-1\:\:(*-2) \\ \\ 5x-2y=10 \\ -2x+2y=2 \\ ------- \\ 3x=12 \\ \\ (3x)/(3)=(12)/(3) \\ \\ x=4 \end{gathered}`

Now, let's plug into the 2nd original equation x=4 and solve it for y:

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

So we know the solution is (4,5).

3) Now, let's graph these equations by setting two t-tables. Let's rewrite those equations from the Standard form to the Slope-intercept form.

5x-2y=10 -2y=10-5x, y=-5+5/2x

x-y=-1,-y=-1-x, y=x+1

4) Now, let's plot those points and trace the lines through them

(-2,-10), (-1,-7.5), (0,-5), (1,-2.5), (2,0)

(-2,-1), (-1,0), (0,1), (1,2), (2,3)