Solve the system of equations using substitution y=3x-2y=-2x+8

Question

asked Aug 15, 2023 45.3k views

1 Answer

Marc Hjorth · Answer 1 · 2023-08-20T21:23:33+0000

We have the following system of equations:

$\begin{gathered} y=3x-2\ldots(A) \\ y=-2x+8\ldots(B) \end{gathered}$

Solving by substitution method.

By substituting equation B into A, we have

Now, by adding 2x to both sides, we get

and by adding 2 to both sides, we get

$\begin{gathered} 10=5x \\ or\text{ equivalently,} \\ 5x=10 \end{gathered}$

Then, by dividing both sides by 5, x is given by

$\begin{gathered} x=(10)/(5) \\ x=2 \end{gathered}$

In order to find y, we can substitute this result into equation (A). It yields,

$\begin{gathered} y=3(2)-2 \\ y=6-2 \\ y=4 \end{gathered}$

Therefore, the solution of the system is x=2 and y=4.