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Section 5.2-12. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).3x-3y = -6-x+2y = 8

Section 5.2-12. Solve the following system of equations by substitution or elimination-example-1
User Arash Khoeini
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1 Answer

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the Given the simultaneous equations


\begin{gathered} 3x-3y=-6\text{ ------(1)} \\ -x+2y=8\text{ -------(2)} \end{gathered}

Solving the above equations by substitution method:

Step 1:

From equation 2, make x the subject of the formula


\begin{gathered} -x+2y=8 \\ \text{making x the subject of formula, we have} \\ x=2y-8\text{ -------(3)} \end{gathered}

Step 2:

Substitute equation 3 into equation 1


\begin{gathered} \text{From equation,} \\ 3x-3y=-6 \\ \text{Thus, we have} \\ 3(2y-8)-3y=-6 \\ \text{opening the brackets, we have} \\ 6y-24-3y=-6 \\ \text{collecting like terms, we have} \\ 6y-3y=-6+24 \\ 3y=18 \\ \text{divide both sides by the coefficient of y.} \\ \text{The coefficient of y is 3. Thus,} \\ y=(18)/(3)=6 \end{gathered}

Step 3:

Substitute the value of y in either equation 1 or 2.


\begin{gathered} \text{From equation 2,} \\ -x+2y=8 \\ \text{Thus,} \\ -x+2(6)=8 \\ -x+12=8 \\ \text{collecting like terms, we have} \\ -x=8-12 \\ -x=-4 \\ x=4 \end{gathered}

Thus, the values of (x, y) are (4, 6)

User Tyler Biscoe
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