About Solving Systems by Elimination:
Another alternative to solve a linear system is known as the elimination method. When we use this method, we first place each equation in standard form. Next, we create a pair of opposite coefficients for one of the variables. By adding the two equations together, one of the variables will be eliminated. We can then solve the resulting linear equation in one variable to obtain one solution. The other variable can be found through substitution or by repeating the elimination step with the other variable.
Test Objectives
- Demonstrate an understanding of a system of linear equations
- Demonstrate the ability to solve a system of linear equations by elimination
- Demonstrate the ability to check the solution for a system of linear equations
#1:
Instructions: Solve each linear system by elimination.
a) $$7x + 10y = 4$$ $$-2x - 5y = -14$$
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#2:
Instructions: Solve each linear system by elimination.
a) $$2x + 5y = 5$$ $$-4x - 10y = -10$$
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#3:
Instructions: Solve each linear system by elimination.
a) $$8x - 32 = -8y$$ $$-y - \frac{5}{3}x = -\frac{32}{3}$$
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#4:
Instructions: Solve each linear system by elimination.
a) $$7y + 34 = -12x$$ $$20 + 8y = -9x$$
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#5:
Instructions: Solve each linear system by elimination.
a) $$-30 + 6x = -14y$$ $$y = -\frac{3}{7}x + \frac{12}{7}$$
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Written Solutions:
#1:
Solutions:
a) $$(-8,6)$$
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#2:
Solutions:
a) $$\text{Infinite Number of Solutions}$$
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#3:
Solutions:
a) $$(10,-6)$$
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#4:
Solutions:
a) $$(-4,2)$$
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#5:
Solutions:
a) $$\text{No Solution}$$