Question

Use one of the algebraic methods tosolve the following system of equations:10x + 4y =-6y = 2x - 6

Answer 1

Using the Substitution method of the simultaneous equation to resolve the system of equations given below

`\begin{gathered} 10x+4y=-6\ldots\ldots\ldots.1 \\ y=2x-6\ldots\ldots\ldots2 \end{gathered}`

Substitute y = 2x - 6 into equation 1 and evaluate for x

`10x+4\mleft(2x-6\mright)=-6`

Simplify

`\begin{gathered} 10x+8x-24=-6 \\ \text{Isolate for x} \\ 18x=-6+24 \\ (18x)/(18)=(18)/(18) \\ \therefore x=1 \end{gathered}`

Substitute x = 1 into equation 2 and evaluate for y

`\begin{gathered} y=2*\: 1-6=2-6=-4 \\ \therefore y=-4 \end{gathered}`

Hence, the solutions to the system of equations are

`x=1,\: y=-4`