facts as shown in the examples below Equations are often written in the context of a geometric situation Write an equation that represents each situation and find
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Mathematical Equations: Examples Using Formulas to Solve for Unknown Variables A mathematical equation must contain the following three essential
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Examples 10x - 3y = 5 and -2x - 4y = 7 are linear equations in two variables The point x = 8 and y = 3 is also a solution of the equation 2x - 3y = 7 since 2(8) - 3(3) = 16 - 9 = 7 The point x = 4 and y = 6 is not a solution of the equation 2x - 3y = 7 because 2(4) - 3(6) = 8 - 18 = -10, and -10 6= 7
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An equation is a mathematical statement that two expressions are equal The solution of an EXAMPLE 1: Solve 5(4t œ 14) œ 7 = 63 Solution: To solve the
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facts as shown in the examples below Equations are often written in the context of a geometric situation Write an equation that represents each situation and find
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, since 4!3=12,!x=3
) or by matching equal quantities, simplifying the equation, and using math facts as shown in the examples below. Equations are often written in the context of a geometric situation. Write an equation that represents each situation and find the value of the variable. Example 1 x+10=32
x=22Example 2 x+2x+8=44
x+2x=36 3x=36 x=12Example 3 3y=25+y
2y=25 y=12.5Example 4 2x+3x+40=180
2x+3x=140
5x=140
x=18 x 10 32 x 2x 8 44 y y y 25 yCore Connections, Course 2 90 Problems Write an equation that represents each situation and then find the value of the variable. 1. 2. 3. 4. 5. 6. Solve each equation. 7. x+7=-9