Question

Y=x+3
y=-x-1
i need to find the solution of equations

Answer 1

`x = - 2 \\ y = 1`

Explanation:

The above are Simultaneous equations.

What are Simultaneous equations?

Simultaneous equations are two or more algebraic equations which share same variables like X,Y or X,Y and Z.

They are called simultaneous equations because they can be solved the same time.

From the question,

`y = x + 3 - - - - - - (1) \\ y = - x - 1 - - - - - - (2) \\ Substitute \: equation \: (2)into \: (1) \\ - x - 1 = x + 3 \\ Collect \: liketerms \\ - x - x = 3 + 1 \\ - 2x = 4 \\ Divide \: bothsides \: by \: - 2 \\ ( - 2x)/( - 2) = (4)/( - 2) \\ x = - 2 \\ Substitute \: the \: value \: of \: x \: into \: equation \: (1) \\ y = x + 3 \\ y = - 2 + 3 \\ y = 1 \\ Therefore \: x = - 2 \: \: and \: y = 1`

Answer 2

`\huge\boxed{\sf \{(-2,1)\}}`

Explanation:

Given equations:

y = x + 3

y = -x - 1

By comparing the above equations, we get:

x + 3 = -x - 1

Add x to both sides

x + x + 3 = -1

2x + 3 = -1

Subtract 3 to both sides

2x = -1 - 3

2x = -4

Divide 2 to both sides

x = -4/2

x = -2

Substitute x = -2 in first equation.

y = x + 3

y = -2 + 3

y = 1

So,

Solution Set = {(x,y)}={(-2,1)}

`\rule[225]{225}{2}`