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NAME DATE PERIOD Lesson 5 Homework Practice Solving Equations with Variables on Each Side Solve each equation. Check your solutions. 1. 3g 12 9g2. 14 m 18 + 12m3. 7c 7 4c + 174. 11t 15 6t5. 20s +
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How to fill out solving systems of equations

01
Start by identifying the variables in the system of equations. Let's say we have two equations with two variables, x and y.
02
Choose one of the equations and solve it for one variable in terms of the other. For example, if we have the equations 2x + 3y = 7 and x - y = 2, we can solve the second equation for x: x = y + 2.
03
Substitute the expression for the solved variable into the other equation. In our example, substitute x = y + 2 into the first equation: 2(y + 2) + 3y = 7.
04
Simplify and solve the resulting equation. In our example, simplify to 2y + 4 + 3y = 7, which gives us 5y + 4 = 7. Solve for y: 5y = 3, y = 3/5.
05
Substitute the value of the solved variable back into one of the original equations to find the value of the other variable. In our example, substitute y = 3/5 into x = y + 2: x = (3/5) + 2, x = 13/5.
06
Check your solution by substituting the values of x and y into both equations to ensure they satisfy both equations.
07
Write down the solution as the ordered pair (x, y). In our example, the solution is (13/5, 3/5).

Who needs solving systems of equations?

01
Solving systems of equations is useful for various fields and professions, including:
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- Engineers: They often need to solve systems of equations to find the values of unknown variables in engineering problems.
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- Economists: Economic models often involve multiple equations that need to be solved simultaneously to understand and predict economic phenomena.
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- Researchers: Solving systems of equations is a valuable tool for researchers in various disciplines, as it allows them to analyze relationships and make predictions based on data.
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Solving systems of equations is the process of finding the values of variables that satisfy multiple equations simultaneously.
Individuals and organizations that need to report their financial data or fulfill specific regulatory requirements may be required to file systems of equations.
To fill out solving systems of equations, one must identify the equations, determine the variables, and apply algebraic methods such as substitution or elimination to find the solutions.
The purpose of solving systems of equations is to find the common values of the variables that satisfy all given equations, which can be used in various applications such as economics, physics, and engineering.
The information reported typically includes the equations involved, the variables being solved, and the resultant values or solutions.
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