Question

Find the solution of the system of equations. x – 3y = -13 2x + 15y = 16

Answer 1

The equation are x-3y=-13 and 2x+15y=16.

The coefficients of y is not equal in both equations.

Multiply the equation x-3y=-13 by 5.

`\begin{gathered} 5(x-3y)=-13\cdot5 \\ 5x-15y=-65 \end{gathered}`

Add the equation 5x-15y=-65 and 2x+15y=16 to eliminate the y.

`\begin{gathered} 5x-15y+2x+15y=-65+16 \\ 7x=-49 \\ x=-(49)/(7) \\ =-7 \end{gathered}`

Substitute 7 for x in the equation x-3y=-13 to obtain the value of y.

`\begin{gathered} -7-3y=-13 \\ -3y=-13+7 \\ y=(-6)/(-3) \\ =2 \end{gathered}`

The solution of the equations is (-7,2).