Question

Use the graph to find the solution y=x+4 y=-2x-2

Answer 1

(-2 , 2)

Explanation:

y=x+4

y=-2x-2

x+4=-2x-2

3x=-6

x=-2

y=2

graph attached

Answer 2

`\large\boxed{\boxed{\pink{\bf \leadsto (-2,2) \ is \ the \ solution \ of \ the \ given \ linear \ equations .}}}`

Explanation:

Given to equations to us are ,

`\qquad \red{\bullet} \: y = x + 4 \\\\\qquad \red{\bullet} \: y = -2x - 2`

And we need to find the solution using graphical method.

So , after plotting the graph of both equations the point where both lines intersect will be the solution of the graph.

And , for plotting we need at least two points .

For equation (1) :-

`\implies y = x + 4`

When x = (-4) .

`\implies y = -4+4\\\\\bf\implies y = 0`

When x = (-3)

`\implies y = -3+4\\\\\bf\implies y = -1`

`\large\boxed{\begin{tabular}c \cline{1-3} \bf x & (-4) & (-3) \\\cline{1-3} \bf y & 0 & 1 \\\cline{1-3}\end{tabular}}`

For equation 2 :-

`\implies y = -2x - 2`

When x = (-1) .

`\implies y = -2(-1)-2\\\\\bf\implies y = 0`

When x = (0)

`\implies y = 0-2\\\\\bf\implies y = -2`

`\large\boxed{\begin{tabular}c \cline{1-3} \bf x & (-1) & 0 \\\cline{1-3} \bf y & 0 & -2 \\\cline{1-3}\end{tabular}}`

Now , let's plot their graphs. Graph is in attachment. Hence on plotting the graph we see that both the lines Intersect on (-2,2) . Hence x = -2 and y = 2 is the solution of the given linear equation.

Hence (-2,2) is the solution of the given pair of linear equations in two variables.