Question

Solve using elimination.–10x + 3y = 2x − 3y = 16

Answer 1

Notice that the coefficient of the variable y in the first equation is +3 and in the second equation is -3. Then, if we add both equations together, they will cancel out.

Add both equations (left member pus left member equals right member plus right member):

`\begin{gathered} -10x+3y=2 \\ x-3y=16 \\ \Rightarrow(-10x+3y)+(x-3y)=2+16 \\ \Rightarrow-10x+3y+x-3y=18 \\ \Rightarrow-10x+x+3y-3y=18 \\ \Rightarrow-9x=18 \end{gathered}`

Notice that we got an equation that just involves the variable x. Solve for x:

`\begin{gathered} \Rightarrow x=(18)/(-9) \\ \Rightarrow x=-2 \end{gathered}`

Replace x=-2 into one of the equations to find the value of y:

`\begin{gathered} -10x+3y=2 \\ \Rightarrow-10(-2)+3y=2 \\ \Rightarrow20+3y=2 \\ \Rightarrow3y=2-20 \\ \Rightarrow3y=-18 \\ \Rightarrow y=-(18)/(3) \\ \Rightarrow y=-6 \end{gathered}`

Therefore, the solution for this system of equations, is:

x = -2 ; y = -6