Question

15) If x and y satisfy both 9x + 2y = 8 and 7x + 2y = 4, then y =? * Hint: Use the elimination method to solve this system of equations

Answer 1

For the information given in the statement you have

`\begin{cases}9x+2y=8\text{ (1)} \\ 7x+2y=4\text{ (2)}\end{cases}`

Using the elimination method, multiply by -1 the equation (2) and then add the equations to eliminate one of the variables

`\begin{cases}9x+2y=8\text{ (1)} \\ 7x+2y=4\text{ (2)}\cdot-1\end{cases}`
`\begin{gathered} \begin{cases}9x+2y=8\text{ (1)} \\ -7x-2y=-4\text{ (2)}\end{cases} \\ ------------- \\ 2x+0y=4 \\ 2x=4 \\ \text{ Divide by 2 on both sides of the equation} \\ (2x)/(2)=(4)/(2) \\ x=2 \end{gathered}`

Now plug the value of x found into any of the initial equations to find the value of y. For example in equation (1)

`\begin{gathered} 9x+2y=8 \\ 9(2)+2y=8 \\ 18+2y=8 \\ \text{ Subtract 18 on both sides of the equation} \\ 18+2y-18=8-18 \\ 2y=-10 \\ \text{ Divide by 2 on both sides of the equation} \\ (2y)/(2)=(-10)/(2) \\ y=-5 \end{gathered}`

Therefore, the solutions of the system of equations are

`\begin{cases}x=2 \\ y=-5\end{cases}`