System of equations: how do i solve this? 3x+2y=10 and 2x-y=9

Answer 1

There are multiple ways of solving systems of linear equations like this. Perhaps the simplest is called substitution. To solve via substitution, solve one equation for a variable. For instance, the second equation, 2x - y = 9 can be solved for y by adding y to both sides and subtracting 9 from both sides. That results in y = 2x - 9.

Since "y" and "2x - 9" are equal, they can be substituted for each other. So now, take the first equation and plug in "2x - 9" wherever there is a "y". This gives us: 3x + 2(2x - 9) = 10. Then multiply out and combine like terms to get 7x - 18 = 10. Add 18 to both sides to get 7x = 28 then divide both sides by 7 to get x = 4.

Using the equation y = 2x - 9, plug in 4 for x to get y = 2(4) - 9 or y = -1

So the solution is x = 4, y = -1 or the ordered pair (4, -1). This is a point that is in common to both of the lines, in other words, it is the intersection point on the graph of the lines.

Answer 2

From the 2nd equation y=2x-9

Substitute into the 1st equation; 3x + 2(2x-9) =7x - 18 =10

7x=28

x=4

y=-1