Solve each system of equations and check your solution. { 2 x-3 y=-7 6 x+5 y=49 .

Name: Problem 51, Chapter 12: Geometry
Uploaded: 2020-06-02T17:08:38-08:00
Duration: 1 min 58 s
Channel: Ashley High
Description: Solve each system of equations and check your solution. { 2 x-3 y=-7 6 x+5 y=49 .

step 1 In this problem, we have a systems of equation, so we have 2x minus 3Y equals negative 7, and we

Solve each system of equations and check your solution. { ...

Key Concepts

Solution Verification

Solution verification is the process of substituting the obtained values back into the original equations to ensure that each equation is satisfied. This step is crucial as it confirms the correctness of the solution and helps to identify any potential mistakes made during the problem-solving process.

System of Linear Equations

A system of linear equations consists of two or more linear equations that share the same set of variables. The goal is to find the specific values of these variables that simultaneously satisfy every equation in the system. This concept is fundamental in algebra and is widely applicable in various fields including economics, engineering, and science.

Elimination Method

The elimination method is a technique used to solve systems of linear equations by strategically adding or subtracting multiples of the equations to cancel out one of the variables. After reducing the system to a single equation in one variable, the value of that variable can be found, and then back-substituted into one of the original equations to solve for the other variable(s).

Substitution Method

The substitution method involves solving one of the equations for one variable in terms of the other(s) and then replacing the corresponding variable in the remaining equations with this expression. This method transforms a system of equations into a single equation with one unknown, making it easier to solve. After finding the value of one variable, it is substituted back into one of the equations to determine the other variable(s).

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