Question

Solve the system by substitution. 4x+3y=5x=4y+6Options: A. The solution is ____B. There are infinitely many solutions. C. There is no solution

Answer 1

So we have the following system of equations:

`\begin{gathered} 4x+3y=5 \\ x=4y+6 \end{gathered}`

We need to solve it by substitution. This means that we have to take the expression for x given by the second equation and replace x with it in the first equation:

`\begin{gathered} 4x+3y=5 \\ 4\cdot(4y+6)+3y=5 \\ 16y+24+3y=5 \\ 16y+3y=5-24 \\ 19y=-19 \\ y=-(19)/(19)=-1 \end{gathered}`

So y=-1. If we use this value in the second equation:

`\begin{gathered} x=4y+6 \\ x=4\cdot(-1)+6 \\ x=-4+6 \\ x=2 \end{gathered}`

So we have x=2 and y=-1 which means that there's one solution. Then the correct answer is A and the solution is (2,-1).