How do you solve a system of linear equations using the substitution method?

Question

Example Question:

Solve the following system of equations using the substitution method:

y=2x+3x

3x - y = 5

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Answer 1

The system is:

y = 2x + 3

3x - y = 5

Since the first equation is already in terms of y, you can substitute it for y in the second equation:

3x - (2x + 3) =5

3x - 2x -3 = 5

x - 3 = 5

x = 8

You can then put the value of x = 8 into the first equation:

y = 2 * 8 + 3

y = 16 + 3

y = 19

Note that you can double-check your calculations by putting x = 8 in the second equation, too:

3 * 8 - y = 5

24 - y = 5

24 = 5 + y

19 = y

The fact that you got the same result means that your calculation was correct. If you got a different result for y, it would mean that you made a mistake somewhere.

The solution is (8, 19)

Answer 2

Solution:

1. Step 1: Substitute the expression for y from the first equation into the second equation.

Since y=2x+3y,

substitute 2x+3 for y in the second equation:

3x−(2x+3)=5

Step 2: Solve the resulting equation for x.

3x−2x−3=5

Simplify:

x−3=5

Add 3 to both sides:

x=8

Step 3: Substitute x=8 back into the first equation to find y

y=2(8)+3

y=16+3

y=19

Solution: The solution to the system of equations is x=8 and y=19.

Final Answer:

(x,y)=(8,19)