Question

1. What is the solution of the system?

y = 2x
x + y = 12
1. (10,2)
2. (8,4)
3. (4,8)

Answer 1

Answer: 3. (4,8)

Explanation:

Step 1:

y = 2x

x + y = 12

Step 2:

In order to create an equation containing only 1 variable, we need to substitute the right side of the first equation for y in the second equation.

In this example, all instances of y in the second equation will be replaced by: 2x

Replacing y with 2x

y = 2x

x + 2x = 12

Step 3:

We need to combine like terms in this expression by adding up all numerical coefficients and copying the literal part, if any.

No numerical coefficient implies a value of 1.

There is only one group of like terms: x,2x

y = 2x

3x = 12

Step 4:

In order to isolate the variable in this linear equation, we need to get rid of the coefficient that multiplies it.

This can be accomplished if both sides are divided by 3.

y = 2x

`(3x)/(3)` =
`(12)/(3)`

Step 5:

We need to reduce this fraction to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

In our example, this is the common factor:3.

y = 2x

x = 4

Step 6:

In order to eliminate x in the first equation, we need to substitute the right side of the second equation for x in the first equation.

In our example, all instances of x in the first equation will be replaced by: 4.

y = 2 × 4

x = 4

Step 7:

Numerical factors in this term have been multiplied.

x = 4

y = 8

Therefore, x = 4 and y = 8.

Answer 2

option 3

Explanation:

y = 2x → (1)

x + y = 12 → (2)

substitute y = 2x into (2)

x + 2x = 12

3x = 12 ( divide both sides by 3 )

x = 4

substitute x = 4 into (1)

y = 2x = 2 × 4 = 8

solution is (4, 8 )