Question

Santiago is solving the system of equations.5x – 4y = 604x + 5y = 60Which description shows a way to solve the system of equations correctly ?

Answer 1

We need to multiply each equation by different factors so that the coefficients next to the x-variable in each new equation are opposite numbers.

Multiplying the first equation by -4, we get:

`\begin{gathered} 5x-4y=60\text{ (eq. 1)} \\ (-4)\cdot(5x-4y)=(-4)\cdot60 \\ (-4)\cdot5x+(-4)\cdot(-4y)=-240\text{ Distributing} \\ -20x+16y=-240\text{ (eq. 3)} \end{gathered}`

Multiplying the second equation by 5, we get:

`\begin{gathered} 4x+5y=60\text{ (eq. 2)} \\ 5\cdot(4x+5y)=5\cdot60 \\ 5\cdot4x+5\cdot5y=300\text{ Distributing} \\ 20x+25y=300\text{ (eq. 4)} \end{gathered}`

And now, the coefficients of the x-variable of equations 3 and 4 are -20 and 20.