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:

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MichellaY334414 MichellaY334414 · Answer 1 · 2022-10-30T18:19:44+01:00

Solution:

Given the system of equations;

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

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

STEP 1: Add equation 1 to equation 2;

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

STEP 2: Divide both sides by -17;

[tex]\begin{gathered} -\frac{17y}{-17}=\frac{102}{-17} \\ y=-6 \end{gathered}[/tex]

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

[tex]\begin{gathered} -4x-3y=-22 \\ -4x-3(-6)=-22 \\ -4x+18=-22 \\ \end{gathered}[/tex]

STEP 4: Subtract 18 from both sides;

[tex]\begin{gathered} -4x+18-18=-22-18 \\ -4x=-40 \end{gathered}[/tex]

STEP 5: Divide both sides by -4;

[tex]\begin{gathered} -\frac{4x}{-4}=-\frac{40}{-4} \\ x=10 \end{gathered}[/tex]

Thus, the solution of the system of equation is;

[tex]x=10,y=-6[/tex]