Write each system of equations in the form { A x+B y=E C x+D y=F . and then solve the

step 1 Here we have to write the equation in standard form that is the given equation in standard form

Write each system of equations in the form { A x+B y=E ...

Write each system of equations in the form $\left\{\begin{array}{l}A x+B y=E \\ C x+D y=F\end{array}\right.$ and then solve the system.
$$\left\{\begin{aligned}
-2 x-y &=-7 \\
\frac{2 x}{3}+\frac{y+1}{2} &=1
\end{aligned}\right.$$

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Key Concepts

Solving Systems of Linear Equations

Solving a system of linear equations entails finding values for the variables that simultaneously satisfy all equations in the system. Common methods include substitution, where one variable is expressed in terms of another, and elimination, where one variable is removed by adding or subtracting equations after appropriate multiplications.

Standard Form of Linear Equations

This concept involves expressing a linear equation in the form Ax + By = E, where A, B, and E are constants. This uniform representation is useful for comparing equations, setting up systems, and applying various strategies like elimination or substitution for solving them.

Clearing Fractions

Clearing fractions means eliminating fractional coefficients by multiplying both sides of an equation by a common denominator. This simplifies the equation to a form with integer coefficients, making it easier to manipulate algebraically, particularly when solving systems of equations.

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