Question

I have to solve each system of equations using elimination or substitution. I don't understand how to do this one.

Answer 1

Given the following system of equations:

`\begin{gathered} 8x+14y=4 \\ -6x-7y=-10 \end{gathered}`

we can solve for 'x' the first equation to get the following:

`\begin{gathered} 8x+14y=4 \\ \Rightarrow8x=4-14y \\ \Rightarrow x=(4-14y)/(8)=(4)/(8)-(14)/(8)y=(1)/(2)-(7)/(4)y \\ x=(1)/(2)-(7)/(4)y \end{gathered}`

now that we have an expression for 'x', we can substitute it on the second equation to get:

`\begin{gathered} -6((1)/(2)-(7)/(4)y)-7y=-10 \\ \Rightarrow-(6)/(2)+(42)/(4)y-7y=-10 \\ \Rightarrow-3+(21)/(2)y-7y=-10 \\ \Rightarrow(21)/(2)y-7y=-10+3=-7 \\ \Rightarrow(7)/(2)y=-7 \\ \Rightarrow y=(-7)/((7)/(2))=-2 \\ y=-2 \end{gathered}`

we have that y = -2, now we can use this value to find 'x':

`\begin{gathered} x=(1)/(2)-(7)/(4)(-2)=(1)/(2)+(14)/(4)=(1)/(2)+(7)/(2)=(8)/(2)=4 \\ x=4 \end{gathered}`

therefore, the solution of the system using substitution is (4,-2)