Question

Solve the system of linear equations3x-2y=-54x + 5y=47

Answer 1

x = 3

y = 7

Step-by-step explanation:

First, we need to take the first equation and solve for y as follows:

`\begin{gathered} 3x-2y=-5 \\ 3x-2y-3x=-5-3x \\ -2y=-5-3x \\ (-2y)/(-2)=(-5-3x)/(-2) \\ y=2.5+1.5x \end{gathered}`

Then, we can replace y with (2.5 + 1.5x) on the second equation, so:

`\begin{gathered} 4x+5y=47 \\ 4x+5(2.5+1.5x)=47_{} \end{gathered}`

So, solving for x, we get:

`\begin{gathered} 4x+5(2.5)+5(1.5x)=47 \\ 4x+12.5+7.5x=47 \\ 11.5x+12.5=47 \\ 11.5x+12.5-12.5=47-12.5 \\ 11.5x=34.5 \\ (11.5x)/(11.5)=(34.5)/(11.5) \\ x=3 \end{gathered}`

Therefore, the value of x is 3.

Finally, we can calculate the value of y as follows:

`\begin{gathered} y=2.5+1.5x \\ y=2.5+1.5(3) \\ y=2.5+4.5 \\ y=7 \end{gathered}`

So, the solution of the system is x = 3 and y = 7