Question

What is the x-coordinate of the solution to the system of linear equations:4x+5y=82x-3y= -18

Answer 1

First, we solve for y the second equation to get the following:

`\begin{gathered} 2x-3y=-18 \\ \Rightarrow2x+18=3y \\ \Rightarrow y=(2x+18)/(3) \end{gathered}`

now we substitute this expression on the irst equation to find the value of the x-coordinate of the solution:

`\begin{gathered} 4x+5\cdot((2x+18)/(3))=8 \\ \Rightarrow4x+(10x+90)/(3)=8 \\ \text{ Multiplying both sides by 3 we get:} \\ (4x+(10x+90)/(3)=8)\cdot3 \\ \Rightarrow12x+10x+90=24 \\ \Rightarrow22x=24-90=-66 \\ \Rightarrow x=-(66)/(22)=-3 \\ x=-3 \end{gathered}`

therefore, x=-3