Question

Graph the system & write its solution
2x+y=-4
Y=-1/2x-1

Answer 1

The solution of system of equation is (-2,0)

Explanation:

Given system of equation are

Equation 1 : 2x+y=(-4)

Equation 2 : y+
`(1)/(2)`x=(-1)

To plot the equation of line, we need at least two points

For Equation 1 : 2x+y=(-4)

Let x=0

2x+y=(-4)

2(0)+y=(-4)

y=(-4)

Let x=1

2x+y=(-4)

2(1)+y=(-4)

y=(-6)

Therefore,

The required points for equation is (0,-4) and (1,-6)

For Equation 2 : y+
`(1)/(2)`x=(-1)

Let x=0

y+
`(1)/(2)`x=(-1)

y+
`(1)/(2)`(0)=(-1)

y=(-1)

Let x=2

y+
`(1)/(2)`x=(-1)

y+
`(1)/(2)`(2)=(-1)

y=(-2)

The required points for equation is (0,-1) and (2,-2)

Now, plot the graph using this points

From the graph,

The red line is equation 1 and blue line is equation 2

Since. The point of intersection is solution of system of equations

The solution of system of equation is (-2,0)