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Solve the system of linear equations by substitution.−x+y=3 and 3x−2y=5

User Gregori
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1 Answer

4 votes

Final answer:

By solving the first equation for y and substituting into the second equation, we find x = 11 and y = 14. Substituting these values back into the original equations confirms that (11, 14) is the correct solution to the system of linear equations.

Step-by-step explanation:

To solve the system of linear equations by substitution, we start with the given equations −x + y = 3 and 3x − 2y = 5. We first solve one of the equations for one variable and then substitute that expression into the other equation.

From the first equation, −x + y = 3, solve for y:

y = x + 3

Now substitute the expression for y into the second equation, 3x − 2y = 5:

3x − 2(x + 3) = 5

Expand and solve for x:

3x − 2x − 6 = 5

x − 6 = 5

x = 11

Now that we have found x, we substitute it back into the expression for y:

y = 11 + 3

y = 14

The solution to the system is (x, y) = (11, 14).

To check the solution, substitute the values back into the original equations:

−(11) + 14 = 3 (True)

3(11) − 2(14) = 5 (True)

Since both statements are true, (11, 14) is indeed the solution to the system of equations.

User MichaelAttard
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