### About Solving Systems of Linear Equations by Substitution:

When we solve a system of linear equations, it is often necessary to use an algebraic method. One such method is known as substitution. With this method, we solve one of the equations for one of the variables. We can then substitute in for this variable in the other equation and proceed to solve our system.

Test Objectives

- Demonstrate the ability to solve a linear equation in two variables for one of the variables
- Demonstrate the ability to substitute in for a variable
- Demonstrate the ability to solve a linear system using substitution

#1:

Instructions: Solve each linear system by substitution.

a) $$y = -5$$ $$3x + 9y = -12$$

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#2:

Instructions: Solve each linear system by substitution.

a) $$-8x + 9y = -37$$ $$17x - 12y = -14$$

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#3:

Instructions: Solve each linear system by substitution.

a) $$30x - 18y = 17$$ $$15x - 9y = -13$$

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#4:

Instructions: Solve each linear system by substitution.

a) $$4x + 6y = -4$$ $$-2x - 6y = -10$$

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#5:

Instructions: Solve each linear system by substitution.

a) $$8x + 4y = -20$$ $$\frac{4}{5}x + \frac{2}{5}y = -2$$

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Written Solutions:

#1:

Solutions:

a) {(11,-5)} : x = 11, y = -5

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#2:

Solutions:

a) {(-10,-13)} : x = -10, y = -13

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#3:

Solutions:

a) No solution : ∅

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#4:

Solutions:

a) {(-7,4)} : x = -7, y = 4

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#5:

Solutions:

a) {(-∞,∞)} : infinitely many solutions