Question

Solve the system of equations using the elimination method. Note that the method of elimination may be referred to as the addition method. (If there is no solution, enter NO SOLUTION.)0.2x + 0.7y = 2.20.9x − 0.2y = 3.2(x, y) =

Answer 1

To solve the system of equations

`\begin{gathered} 0.2x+0.7y=2.2 \\ 0.9x-0.2y=3.2 \end{gathered}`

we need to make the coefficients of one of the variables opposite, that is, they need to have the same value with different sign; let's do this with the y variable, so let's multiply the second equation by 0.7 and the first equation by 0.2; then we have:

`\begin{gathered} 0.04x+0.14y=0.44 \\ 0.63x-0.14y=2.24 \end{gathered}`

Now we add the equations and solve the resulting equation for x:

`\begin{gathered} 0.04x+0.14y+0.63x-0.14y=0.44+2.24 \\ 1.64x=2.68 \\ x=(2.68)/(0.67) \\ x=4 \end{gathered}`

Now that we have the value of x we plug it in one of the original equations and solve for y:

`\begin{gathered} 0.2(4)+0.7y=2.2 \\ 0.8+0.7y=2.2 \\ 0.7y=2.2-0.8 \\ 0.7y=1.4 \\ y=(1.4)/(0.7) \\ y=2 \end{gathered}`

Therefore, the solution of the system of equation is (4,2)