Question

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Solve the system of equations using the substitution method. Make sure to check your solution.

y = 3x + 2

-4x + 4y = 16

In the blanks below, type just the number for the x-coordinate in blank 1 and just the number for the y-coordinate in blank 2.

x-coordinate:
y-coordinate:

Answer 1

y = 5

x = 1

Explanation:

y = 3x + 2

-4x + 4(3x+2)=16

y=3x+2

-4x+(4*3x+4*2)=16

x = 1

y = 5

Answer 2

x-coordinate = 1

y-coordinate = 5

Explanation:

By using the substitution method, we substitute either x-term or y-term in any equation.

the term must be only the subject in order to substitute in.

Our equation that has only the subject is the first equation.

Substitute y = 3x+2 in the second equation.

`- 4x + 4(3x + 2) = 16`

Distribute 4 in 3x+2

`- 4x + 12x + 8 = 16`

The constant cannot add up or subtract with the variable. Therefore, move 8 to subtract 16 on another side.

`12x - 4x = 16 - 8 \\ 8x = 8`

Move 8 to divide 8 on the another side.

`x = (8)/(8) \\ x = 1`

Our next goal is to find the y-value by substituting x = 1 in any given equation.

I will substitute x = 1 in the first equation. (You can substitute in the second equation if you want.)

`y = 3(1) + 2 \\ y = 3 + 2 \\ y = 5`

Answer Check

Checking is to make sure that we have got the right answer. We can check the answer by substituting y-value and x-value in both equations.

`x = 1 \\ y = 5`

First Equation Check

`5 = 3(1) + 2 \\ 5 = 3 + 2 \\ 5 = 5`

The equation is true. Therefore, the answer is correct for first equation.

Second Equation Check

`- 4(1) + 4(5) = 16 \\ - 4 + 20 = 16 \\ 16 = 16`

The equation is true. Both equations are true for x = 1 and y = 5.

Therefore, the answer is (1,5)