Question

For the following problem, the answers is given. Show the calculations that are needed to get to the answer.ProblemSolutionSolve this system of equations:X = 10a) - 4x - 3y = -22y = -6b) 4x - 14y = 124Show your work here:

Answer 1

Given the system of equations;

`\begin{gathered} -4x-3y=-22\ldots\ldots\ldots\text{.equation}1 \\ 4x-14y=124\ldots.\ldots\text{.}\mathrm{}\text{equation}2 \end{gathered}`

We would show calculation that lead to the answer by elimination method.

STEP 1: Add equation 1 to equation 2;

`\begin{gathered} -4x+4x-3y+(-14y)=-22+124 \\ -17y=102 \end{gathered}`

STEP 2: Divide both sides by -17;

`\begin{gathered} -(17y)/(-17)=(102)/(-17) \\ y=-6 \end{gathered}`

STEP 3: Substitute the value of y in equation 1;

`\begin{gathered} -4x-3y=-22 \\ -4x-3(-6)=-22 \\ -4x+18=-22 \\ \end{gathered}`

STEP 4: Subtract 18 from both sides;

`\begin{gathered} -4x+18-18=-22-18 \\ -4x=-40 \end{gathered}`

STEP 5: Divide both sides by -4;

`\begin{gathered} -(4x)/(-4)=-(40)/(-4) \\ x=10 \end{gathered}`

Thus, the solution of the system of equation is;

`x=10,y=-6`