Question

Which ordered pair is a solution to the system of linear equations?

2x + 3y= 6

–3x + 5y = 10

Answer 1

Both write the equation in the form of directional .

2x + 3y = 6
3y = - 2x + 6

`y = - (2)/(3) x + 2`

a = - 2/3 b = 2
...............................................................

-3x + 5y = 10
5y = 3x + 10

`y = (3)/(5) x + 2`

a = 3/5 b= 2
.....................................
b ratio is the same , so the two lines intersect the y-axis at P = ( 0,2 ) . This joint solution

Answer 2

The solution to the system of linear equations is (0,2)

Explanation:

1. Let´s name the two equations given as:

`2x+3y=6 (Eq.1)\\-3x+5y=10 (Eq.2)`

2. Solve for y on Eq.1:

`2x+3y=6\\3y=6-2x\\y=(6-2x)/(3) (Eq.3)`

3. Replace Eq.3 in Eq.2:

`-3x+5((6-2x)/(3))=10\\-3x+(30-10x)/(3)=10\\-3x+(30)/(3)-(10x)/(3)=10\\ -3x+10-(10x)/(3)=10\\-3x-(10x)/(3)=10-10\\-3x-(10x)/(3)=0\\(-9x-10x)/(3)=0\\ -9x-10x=0\\-19x=0\\x=0`

4. Replace the value of x on Eq.3:

`y=(6-2(0))/(3)\\y=(6)/(3)\\y=2`

Therefore the solution to the system of linear equations is (0,2)