Question

Show how to use substitution or elimination to solve the following system of equations. Write the solution as an ordered pair.

4x-y=10
Y=2x-2

Answer 1

The solution to the system of equations using substitution is (4, 6), where x is substituted first followed by finding the value of y.

Step-by-step explanation:

To solve the given system of equations using substitution, we can take the second equation, Y=2x-2, and substitute it into the first equation 4x - y = 10. After substituting we get 4x - (2x-2) = 10. This simplifies to 2x+2 = 10, and then further simplifying gives us x = 4. Once we have the value of x, we substitute it back into Y=2x-2 to find the value of y. This would give us Y = 2(4) - 2, resulting in y = 6. Therefore, the solution of the system of equations as an ordered pair is (4, 6).

Answer 2

(4, 6)

Step-by-step explanation:

Substitution

Using the second equation, we can substitute for y in the first equation.

4x -(2x-2) = 10

2x +2 = 10 . . . . simplify

x +1 = 5 . . . . . . .divide by 2

x = 4 . . . . . . . . . subtract 1

y = 2(4) -2) = 6 . . . . substitute for x in the equation for y

The solution is (x, y) = (4, 6).

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Elimination

Often, we like to start with both equations in standard form when we solve by elimination. That is nice, but not completely necessary.

We can eliminate the y-variable by simply adding the two given equations.

(4x -y) +(y) = (10) +(2x -2)

4x = 8 + 2x . . . . . collect terms. The y-variable has been eliminated.

2x = 8 . . . . . . . . . subtract 2x

x = 4 . . . . . . . . . . divide by 2

Y can be found using the second equation.

(x, y) = (4, 6)

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We could have eliminated the x-variable by multiplying the second equation by 2, then adding the two equations.

(4x -y) +2(y) = (10) +2(2x -2)

y = 6 . . . . . . . . . subtract 4x from both sides. The x-variable has been eliminated.

Now, x can be found using either equation.

6 = 2x -2 . . . substitute for y in the second equation

3 = x - 1 . . . divide by 2

x = 4 . . . . . add 1

(x, y) = (4, 6)