Question

Solve the system of equations by graphing.
x+y=1
4x+y=-19

Answer 1

( -6.667 ,7.667) is the intersection point.

Explanation:

We have system of equations.

x+y=1 (eq 1)

4x+y=-19 (eq 2)

In first equation,

y = -x+1

slope = -1 and y-intercept = 1.

in second equation,

y = -4x-19

slope = -4 and y-intercept = -19.

In graph,the intersecting point is the solution of system of equations.

The intersecting point is ( -6.667 ,7.667).

the graph is attached .

Answer 2

The solution of the given system of equations is (-6.667,7.667).

Explanation:

The given equations are

`x+y=1` ...(1)

`4x+y=-19` ....(2)

put x=0 to find the y-intercept.

`0+y=1`

`y=1`

Therefore y-intercept of equation (1) is (0,1).

`4(0)+y=-19`

`y=-19`

Therefore y-intercept of equation (2) is (0,-19).

put y=0 to find the y-intercept.

`x+0=1`

`x=1`

Therefore x-intercept of equation (1) is (1,0).

put y=0 to find the y-intercept.

`4x+(0)=-19`

`x=-(19)/(4)`

Therefore x-intercept of equation (1) is (-4.75,0).

Draw the graph of both lines by joining their x and y-intercept.

From the graph it is noticed that both the line intersect each other at (-6.667,7.667).

Therefore solution of the given system of equations is (-6.667,7.667).