Question

What is the solution of this system of linear equations? 3y = x + 6 y – x = 3 (3, 6) (2, 1) no solution infinite number of solutions

Answer 1

Here's the answer. I hope I have understood you right :)

Answer 2

Answer:

As you have written the equations, the solution is (-1.5, 1.5).

Step-by-step explanation:

As written, the system of equations is

$\left \{ {{3y=x+6} \atop {y-x=3}} \right.$

To solve this, we will use substitution.  First we will isolate y in the second equation:

y-x = 3

Add x to each side:

y-x+x = 3+x

y = 3+x

Now we will substitute this into the first equation

3y = x+6

3(3+x) = x+6

Using the distributive property,

3(3)+3(x) = x+6

9+3x = x+6

Subtract x from each side:

9+3x-x = x+6-x

9+2x = 6

Subtract 9 from each side:

9+2x-9 = 6-9

2x = -3

Divide both sides by 2:

2x/2 = -3/2

x = -1.5

Substitute this into the second equation:

y-(-1.5) = 3

y+1.5 = 3

Subtract 1.5 from each side:

y+1.5-1.5 = 3-1.5

y = 1.5