Question

Solve the following system of equations by using the substitution method.

x – y = 3
2x + 2y = 2

(3, 4)

(-4, 5)

(2, -1)

Answer 1

3,4 would be the answer

Answer 2

Given equations,
`x-y=3\\2x+2y=2`

Applying Substitution method to solve the equation.

Solve the first equation
`x-y=3` for x,

`x-y=3\:\Rightarrow x=3+y`

Substitute the value of x in second equation,

`2x+2y=2\\\\\Rightarrow 2(3+y)+2y=2\\\\\Rightarrow 6+2y+2y=2\\\\\Rightarrow6+4y=2\\\\\Rightarrow4y=2-6\\\\\Rightarrow4y=-4\\\\\Rightarrow y=(-4)/(4) =-1\\\\\Rigtharrow y=-1`

To calculate the value of x substitute the value of y in first equation

`x-y=3\\\\\Rightarrow x-(-1)=3\\\\\Rightarrow x=3-1=2\\\\\Rightarrow x=2`

Hence, the solution of the equations
`x-y=3\\2x+2y=2` is (2,-1).