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
$y = - \frac{2}{3} x + 2$

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

-3x + 5y = 10
5y = 3x + 10
$y = \frac{3}{5} x + 2$

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

Answer:

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

Step-by-step 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:

$2x+3y=6\\3y=6-2x\\y=\frac{6-2x}{3} (Eq.3)$

3. Replace Eq.3 in Eq.2:

$-3x+5(\frac{6-2x}{3})=10\\-3x+\frac{30-10x}{3}=10\\-3x+\frac{30}{3}-\frac{10x}{3}=10\\ -3x+10-\frac{10x}{3}=10\\-3x-\frac{10x}{3}=10-10\\-3x-\frac{10x}{3}=0\\\frac{-9x-10x}{3}=0\\ -9x-10x=0\\-19x=0\\x=0$

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

$y=\frac{6-2(0)}{3}\\y=\frac{6}{3}\\y=2$

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