Question

solve the system using the subsition method (if there is no solution enter no solution if there are infinite put infinite)Y=2x-74x + y =17

Answer 1

To solve the system of equations by the substitution method, choose any variables and solve for any equations.

`\begin{cases}y=2x-7\Rightarrow\text{ Equation 1} \\ 4x+y=17\Rightarrow\text{ Equation 2}\end{cases}`

As you can see in Equation 1, the variable y is already solved:

`y=2x-7\Rightarrow\text{ Equation 1}`

Now, substitute the value of y in Equation 2:

`\begin{gathered} 4x+y=17\Rightarrow\text{ Equation 2} \\ 4x+2x-7=17 \end{gathered}`

Now, we can solve the above equation for x:

`\begin{gathered} 4x+2x-7=17 \\ \text{ Add similar terms to the left side of the equation} \\ 6x-7=17 \\ \text{ Add 7 from both sides of the equation} \\ 6x-7+7=17+7 \\ 6x=24 \\ \text{ Divide by 6 from both sides of the equation} \\ (6x)/(6)=(24)/(6) \\ \boldsymbol{x=4} \end{gathered}`

Finally, we replace the value of x in any of the initial equations, for example, in Equation 1:

`\begin{gathered} y=2x-7\Rightarrow\text{ Equation 1} \\ y=2\cdot4-7 \\ y=8-7 \\ \boldsymbol{y=1} \end{gathered}`

Therefore, the solution of the given system of equations is

`\begin{cases}\boldsymbol{x=4} \\ \boldsymbol{y=1}\end{cases}`