3. Solve the following system of equations by

and check your answer.

a) Graphing

 

Solve the first equation for y.

 

 

Solve the second equation for y.

 

 

 

Graph both equations,

 

 

 

and we see that the solution is (3, -1) or x = 3 and y = -1.

 

Check

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Substitute these numbers into the two equations. When we substitute them into the first equation we get

 

(3) + (-1) = 0

3 - 3 = 0

 

and it checks.

In the other equation we get

 

3(3) + 2(-1) = 7

9 - 2 = 7

 

and they both check

 

b) Substitution

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Solve one of the equations for one of the unknowns. The simplest

unknown would be the x in the first equation. Solve the first

equation for x

 

 

Substitute this in for x in the other equation.

 

 

This gives us an equation in only one unknown. Solve this equation.

 

 

 

 

 

The simplest way to find x is to substitute this solution into

the equation where we expressed x as a function of y.

 

 

 

c) Addition

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We need to get the multiply both sides of our equations by

suitable numbers so that the coefficients of one of the unknowns

match up. Multiply the top equation by 3 and the bottom equation

by -1.

 

 

 

 

To find x, substitute this solution into either one of the original

equations. The simplest would be the first equation.

 

 

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