Question

What is the solution to the system of equations?2x + 3y = 263x + 5y = 40A.x = 10, y = 2B.x = 10, y = –2C.x = –10, y = –2

Answer 1

`x\text{ = 10 , y = 2}`

Here, we want to solve the system of linear equations simultaneously

We are going to use the elimination method here

We multiply the first equation by 3 and the second by 2

We have this as follows;

`\begin{gathered} 3*\text{ (2x+ 3y = 26} \\ 2\text{ }*\text{ (3x + 5y = 40} \\ \\ 6x\text{ + 9y = 78} \\ 6x\text{ + 10y = 80} \\ \\ \text{Subtract equation i from i}i \\ 10y-9y\text{ = 80-78} \\ y\text{ = 2} \end{gathered}`

To get the value of x, we substitute the value of y into any of the initial equations

Let us use the first equation. We have this as;

`\begin{gathered} 2x\text{ + 3(2) = 26} \\ 2x\text{ + 6 = 26} \\ 2x\text{ = 26-6} \\ 2x\text{ = 20} \\ x\text{ = }(20)/(2) \\ x\text{ = 10} \end{gathered}`