Question

Verify that each system of equations has the indicated solution. $\left\{\begin{array}{r}-x-2 y=5 \\ -2 x+y=-5\end{array}\right.$ Solution: $x=1, y=-3$

   Verify that each system of equations has the indicated solution.
$\left\{\begin{array}{r}-x-2 y=5 \\ -2 x+y=-5\end{array}\right.$
Solution: $x=1, y=-3$

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 8, Problem 8

Instant Answer

Solved by Expert Vipender Yadav

04/16/2020

Step 1

Step 1: We are given the system of equations: \[ \begin{cases} -x-2y=5\\ -2x+y=-5 \end{cases} \] We are also given the solution $x=1, y=-3$ and we need to verify this solution. Show more…

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Verify that each system of equations has the indicated solution. $\left\{\begin{array}{r}-x-2 y=5 \\ -2 x+y=-5\end{array}\right.$ Solution: $x=1, y=-3$

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The solution to such a system is the set of variable values that satisfy every equation simultaneously, representing the point or points where the equations intersect when graphed.

Solution Verification

Solution verification involves substituting the proposed values for the variables back into each equation of the system to ensure that every equation holds true. This method confirms whether the provided solution is correct by checking the equality on both sides of each equation.

Substitution Technique

The substitution technique is a method used to verify or solve a system of equations by replacing the variable with a given value or an expression derived from one equation. This technique simplifies the process of checking if the solution set satisfies all equations, ensuring the consistency of the solution across the entire system.

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