Question

Is (1,4) a solution to the system:

y=3x+1

y=-x+5

Answer 1

To find:-

• Whether (1,4) is a solution to the given system of equations.

Answer:-

The given system of equation is ,

`\begin{cases}y = 3x + 1 \dots (\rm 1 ) \\ y = -x + 5 \dots (\rm 2) \end{cases}`

This given set of equations are linear equations in two variables , which can be solved by various methods like elimination method and substitution method .

We would use here substitution.

We cam here substitute the value of
`y` from equation 1 into equation 2 as ,

`\implies y = - x + 5`

`\implies 3x + 1 = - x + 5`

Now solve for
`x` ,

`\implies 3x + x = 5 - 1`

`\implies 4x = 4`

`\implies x =(4)/(4)`

`\implies x = 1`

Now substitute this value of
`x` into equation 2 to find out
`y` as ,

`\implies y = -1 + 5`

`\implies y = 4`

Hence we got our answer as , x = 1 and y = 4 , which is the solution to the given set of equations.

Hence we conclude that (1,4) is a solution to the system of equations.

Yes , (1,4) is a solution .

and we are done!