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Komok [63]
1 year ago
11

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
Mathematics
1 answer:
zvonat [6]1 year ago
5 0

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=-\frac{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).

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