Question

Solve the following system of equation using substitution4x + 2y = 10?/1x - y = 13What is the solution for x?

Answer 1

x = 6

Step-by-step explanation

The substitution method consists on taking one equation to solve for one variable as a function of the other. Then substitute that variable with the expression we find in the other equation and then solve for that other variable.

In this case, we want to solve for x, so we'll take one of the equations and find y as a function of x. For the second equation:

`\begin{gathered} x-y=13 \\ y=x-13 \end{gathered}`

Now we replace y by x - 13 in the first equation:

`4x+2(x-13)=10`

And solve for x:

`\begin{gathered} 4x+2x-2\cdot13=10 \\ 6x-26=10 \\ 6x=10+26 \\ 6x=36 \\ x=(36)/(6) \\ x=6 \end{gathered}`