Question

Solve the system of equations below. You may want to use the method by substitution starting with the second equation. 3x−2y =105x+10y =−10

Answer 1

As given by the question

There are given that the system of the equation

`\begin{gathered} 3x-2y=10\ldots(1) \\ 5x+10y=-10\ldots(2) \end{gathered}`

Now,

From equation (1), find the value of x

`\begin{gathered} 3x-2y=10 \\ 3x=10+2y \\ x=(10+2y)/(3)\ldots(3) \end{gathered}`

Then,

Put the value of x into the equation (2)

So,

`\begin{gathered} 5x+10y=-10 \\ 5((10+2y)/(3))+10y=-10 \\ (50+10y)/(3)+10y=-10 \\ (50+10y+30y)/(3)=-10 \\ 50+10y+30y=-30 \\ 50+40y=-30 \\ 40y=-30-50 \\ 40y=-80 \\ y=-2 \end{gathered}`

Now,

Put the value of y into the equation (3)

So,

From the equation (3)

`\begin{gathered} x=(10+2y)/(3) \\ x=(10+2(-2))/(3) \\ x=(10-4)/(3) \\ x=(6)/(3) \\ x=2 \end{gathered}`

Hence, the value of x is 2, and the value of y is -2.