Question

The system shown has _____ solution(s).

y = x + 1
2y - x = 2

no
one
infinite

Answer 1

This system has one solution. Here are my steps to solving this problem:

y=x+1

2(x+1) - x = 2

2x +2 - x = 2

2x - x + 2 = 2

x + 2 = 2
- 2 - 2
----------------
x = 0

y = 0 + 1
y = 1

I hope this helps you!

Answer 2

The system has one solution i.e., (0,1).

Explanation:

Given : The system of equations
`y=x+1` and
`2y-x=2`

To find : The system shown has _____ solution(s)?

Solution :

We solve the system of equations by substitution method,

Let
`y=x+1` .....(1)

`2y-x=2` ......(2)

Substitute the value of y of equation (1) into (2)

`2y-x=2`

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

`2x+2-x=2`

`x=0`

Substitute in equation (1)

`y=x+1`

`y=0+1`

`y=1`

Therefore, The system has one solution i.e., (0,1).