Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

16. On your own paper, graph the following system of equations. Describe the graphs (perhaps give a few points on each line) and give the solution to the system of equations.
-2x - 5y = 20
y=4/5x+2


Sagot :

Answer:

(-5, 2)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-2x-5y=20\\y=\dfrac{4}{5}x+2\end{cases}[/tex]

Both equations are linear equations.

Equation 1

Rearrange Equation 1 to make y the subject:

[tex]\implies -2x-5y=20[/tex]

[tex]\implies -5y=2x+20[/tex]

[tex]\implies y=-\dfrac{2}{5}x-4[/tex]

Therefore, the graph of this equation is a straight line with a negative slope and a y-intercept of (0, -4).

Find two points on the line by substituting two values of x into the equation:

[tex]x = 0\implies y=-\dfrac{2}{5}(0)-4=-4 \implies (0,-4)[/tex]

[tex]x = 5 \implies y=-\dfrac{2}{5}(5)-4=-6 \implies (5,-6)[/tex]

Plot the found points and draw a straight line through them.

Equation 2

The graph of this equation is a straight line with a positive slope and a y-intercept of (0, 2).

Find two points on the line by substituting two values of x into the equation:

[tex]x = 0 \implies y=\dfrac{4}{5}(0)+2=2 \implies (0,2)[/tex]

[tex]x = 5 \implies y=\dfrac{4}{5}(5)+2=6 \implies (5,6)[/tex]

Plot the found points and draw a straight line through them.

Solution

The solution(s) to a system of equations is the point(s) of intersection.

From inspection of the graph, the point of intersection is (-5, -2).

To verify the solution, substitute the second equation into the first and solve for x:

[tex]\implies \dfrac{4}{5}x+2=-\dfrac{2}{5}x-4[/tex]

[tex]\implies \dfrac{6}{5}x=-6[/tex]

[tex]\implies 6x=-30[/tex]

[tex]\implies x=-5[/tex]

Substitute the found value of x into one of the equations and solve for y:

[tex]\implies \dfrac{4}{5}(-5)+2=-2[/tex]

Hence verifying that (-5, -2) is the solution to the given system of equations.

Learn more about systems of equations here:

https://brainly.com/question/27357423

https://brainly.com/question/27034625

View image semsee45

First simplify first one

  • -2x-5y=20
  • 5y=-2x-20
  • y=-2/5x-4

Another one is

  • y=4/5x+2

On first line

at x=0

  • y=-4

At x=5

  • y=-2-4=-6

On second line

At x=0

  • y=2

At x=5

  • y=20+2=22

Graph attached

Solution is (-5,-2)

View image MisterBrainly
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.