Solve the system of linear equations by graphing.

y = –x – 7

x + 2y = 4

What is the solution to the system of linear equations?

(–4.5, 4.25)
(–1.7, –2.8)
(0, –7)
(3, 0.5)

Question

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Respuesta :

carlosego carlosego · Answer 1 · 2019-07-10T21:40:47+02:00

For this case we have the following system of equations:

[tex]y = -x-7\\x+2y = 4[/tex]

Substituting the first equation in the second one we have:

[tex]x+2 (-x-7) = 4\\x-2x-14 = 4\\-x = 4 14\\-x = 18\\x = -18[/tex]

We find the value of y:

[tex]y = - (- 18) -7\\y = 18-7\\y = 11[/tex]

Thus, the solution of the system is:

(-18,11)

Answer:

(-18,11)

Answer Link

luisejr77 luisejr77 · Answer 2 · 2019-07-10T21:45:42+02:00

Answer: (-18,11)

Step-by-step explanation:

Find the x-intercept of the first equation by substituting [tex]y=0[/tex] and solving for "x":

[tex]y = -x - 7\\\\x=-7[/tex]

Find the y-intercept of the first equation by substituting [tex]x=0[/tex] and solving for "y":

[tex]y = -x - 7\\\\y=0-7+\\\\y=-7[/tex]

Graph the line passing through the points (-7,0) and (0,-7)

Find the x-intercept of the second equation by substituting [tex]y=0[/tex] and solving for "x":

[tex]x + 2y = 4\\\\x + 2(0) = 4\\\\x=4[/tex]

Find the y-intercept of the second equation by substituting [tex]x=0[/tex] and solving for "y":

[tex]x + 2y = 4\\\\0 + 2y = 4\\\\y=2[/tex]

Graph the line passing through the points (4,0) and (0,2)

You can observe in the graph that the point of intersection of the lines is:

(-18,11)

This is the solution of the system of equations.