Solve the below system of equations using the linear combination method. Show all your work, explaining each step in solving the system using the linear combination method. 2x + 3y = 1 y = -2x - 9 Please respond to the questions using your own words with proper explanations and use of math vocabulary. Use ACE Strategy to answer the equation:

In Linear Combination method, the co-efficient of any one variable in the equation is made opposite to each other so that it might cancel out later by adding the equations

Given equations are:

[tex]2x + 3y = 1\ \ \ \ Eqn1\\y = -2x-9\\2x-y = -9\ \ \ \ \ Eqn2[/tex]

We can see that the coefficient of x is already same, we have to multiply the second equation by -1 to make the co-efficient opposite

So,

Multiplying Equation 2 by -1

[tex]-2x-y=9\ \ \ \ Eqn3[/tex]

Adding Equation 1 and Equation 3

[tex]2x+3y-2x-y = 1+9\\2y = 10[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2} = \frac{10}{2}\\y = 5[/tex]

Putting y = 5 in equation 1

[tex]2x+3(5) = 1\\2x+15 = 1\\2x = 1-15\\2x = -14[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2} = \frac{-14}{2}\\x = -7[/tex]

Hence,

The solution is (-7,5)

Keywords: Linear equations, variables

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