Question

6 Use elimination to solve eachsystem of equations3x + 5y = -23x - 2y = - 16

Answer 1

x = -4

y = 2

Explanation:

Given the below system of equations;

`\begin{gathered} 3x+5y=-2\ldots.\ldots\ldots\text{.Equation 1} \\ 3x-2y=-16\ldots\ldots\ldots\text{.}\mathrm{}\text{Equation 2} \end{gathered}`

We'll go ahead and solve the above system of equations using the elimination method following the below steps;

Step 1: Subtract Equation 2 from Equation 1;

`\begin{gathered} (3x-3x)+\lbrack5y-(-2y)\rbrack=\lbrack-2-(-16)\rbrack \\ 0+(5y+2y)=-2+16 \\ 7y=14 \end{gathered}`

Step 2: Divide both sides by 7;

`\begin{gathered} (7y)/(7)=(14)/(7) \\ y=2 \end{gathered}`

Step 3: Substitute y in Equation 1 with 2

`\begin{gathered} 3x+5(2)=-2 \\ 3x=-2-10 \\ (3x)/(3)=-(12)/(3) \\ x=-4 \end{gathered}`

So the solution to the given system of equation is x = -4 and y = 2