Question

What is the value of the y-coordinate of the solution of the given system? 4x + 3y = 33 3x + 2y = 23

Answer 1

The system of equations given is solved as follows;

`\begin{gathered} 4x+3y=33---(1) \\ 3x+2y=23---(2) \\ \text{Multiply equation (1) by 3, and multiply equation (2) by 4} \\ 12x+9y=99---(3) \\ 12x+8y=92---(4) \\ \text{Subtract equation (4) from equation (3)} \\ (12x-12x)+(9y-8y)=99-92 \\ 0+y=7 \\ y=7 \\ \text{Substitute for the value of y into equation (1)} \\ 4x+3y=33 \\ 4x+3(7)=33 \\ 4x+21=33 \\ \text{Subtract 21 from both sides} \\ 4x=12 \\ \text{Divide both sides by 4} \\ x=3 \end{gathered}`

The value of y therefore is 7