Question

6x+5y=46x+y=-20how do you solve doing systems if elimination

Answer 1

Given the equation system:

`\begin{cases}6x+5y=4 \\ 6x+y=-20\end{cases}`

To solve an equation system the first step is to make sure that the leading coefficients are the same, which means, that the first term of the equations must be multiplied by the same number. If they are not, you have to multiply one or both equations by a number so that the leading coefficient is the same.

For the given equation system, both equations start with 6x, so the leading coefficient is the same.

The second step is to subtract both equations. You have to calculate the difference between the like terms of both expressions:

The resulting equation is 4y=24, from this equation you can calculate the value of y, to do so you have to divide both sides by 4:

`\begin{gathered} 4y=24 \\ (4y)/(4)=(24)/(4) \\ y=6 \end{gathered}`

Finally, replace the value of y into either one of the original equations to determine the value of x:

`\begin{gathered} 6x+y=-20 \\ 6x+6=-20 \end{gathered}`

-Pass 6 to the right side by subtracting it from both sides of the equation:

`\begin{gathered} 6x+6-6=-20-6 \\ 6x=-26 \end{gathered}`

-And divide both sides by 6 to reach the value of x:

`\begin{gathered} (6x)/(6)=-(26)/(6) \\ x=-(13)/(3) \end{gathered}`

So the solution of this equation system is

`(-(13)/(3),6)`