Question

Solve the system of linear equations by graphing.

Answer 1

Answer: (-18,11)

Step-by-step explanation:

Find the x-intercept of the first equation by substituting $y=0$ and solving for "x":

$y = -x - 7\\\\x=-7$

Find the y-intercept of the first equation by substituting $x=0$ and solving for "y":

$y = -x - 7\\\\y=0-7+\\\\y=-7$

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

Find the x-intercept of the second equation by substituting $y=0$ and solving for "x":

$x + 2y = 4\\\\x + 2(0) = 4\\\\x=4$

Find the y-intercept of the second equation by substituting $x=0$ and solving for "y":

$x + 2y = 4\\\\0 + 2y = 4\\\\y=2$

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.

Answer 2

For this case we have the following system of equations:

$y = -x-7\\x+2y = 4$

Substituting the first equation in the second one we have:

$x+2 (-x-7) = 4\\x-2x-14 = 4\\-x = 4 14\\-x = 18\\x = -18$

We find the value of y:

$y = - (- 18) -7\\y = 18-7\\y = 11$

Thus, the solution of the system is:

(-18,11)

Answer:

(-18,11)