Question

Sove each system of equations using substitution. y = x +1 y = 2x-1

Answer 1

The system of equations we have is:

`\mleft\{\begin{aligned}y=x+1 \\ y=2x-1\end{aligned}\mright.`

Step 1. We need to use the substitution method, for this, we substitute the second equation in the place of the "y" in the first equation.

We get the following expression:

`2x-1=x+1`

Now we solve this equation for x.

Step 2. Substract x from both sides of the equation:

`\begin{gathered} 2x-x-1=x-x+1 \\ x-1=1 \end{gathered}`

Step 3. Add 1 to both sides of the equation:

`\begin{gathered} x-1+1=1+1 \\ x=2 \end{gathered}`

Step 4. Find the value of y using the first equation of the system:

`y=x+1`

since x=2, we get:

`\begin{gathered} y=2+1 \\ y=3 \end{gathered}`

Answer:

`\begin{gathered} x=2 \\ y=3 \end{gathered}`