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 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
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 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

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 Ineq. #9:

 Solve for:

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# Solving Linear Systems of Equations by Substitution

Example

Use substitution to find the solution of this system.

 -3x + 4y x - 6y = 17= -8 First equation Second equation

Solution

Step 1 Solve one equation for one of the variables in terms of the other variable.

 Either equation may be solved for either variable. For instance, letâ€™s solve the second equation for x. Add 6y to both sides. x - 6y x = -8 = 6y - 8

Step 2 Substitute the expression found in Step 1 into the other equation. Then, solve for the variable.

 Substitute 6y - 8 for x in the first equation. Remove parentheses. Combine like terms. Subtract 24 from both sides. Divide both sides by -14. Now we know . Next, we will find x. -3x + 4y -3(6y - 8) + 4y  -18y + 24 + 4y -14y + 24 -14y y = 17= 17 = 17 = 17 = -7 Step 3 Substitute the value obtained in Step 2 into one of the equations containing both variables. Then, solve for the remaining variable.

 We will use the equation from Step 1. x = 6y - 8 Substitute for y. x Simplify. The solution of the system is x = -5

Step 4 To check the solution, substitute it into each original equation. Then simplify.

Substitute -5 for x and for y into each original equation.

Then simplify.

In each case, the result will be a true statement.

The details of the check are left to you.

Note:

If we graphed the system, the lines would intersect at the point 