Given the equation - 3x +2y =4. Write another linear equation that will form a linear system with exactly one solution?
I usually try to answer b4 i ask question But this time i'm really stuck. plz help ?
Any other line that intersects that one will do. It can not be the same line and it can not be parallel. You have
-3 x + 2 y = 4
so change the sign of the x coefficient for example which changes the slope.
+3 x + 2 y = 4
Now you have
-3 x + 2 y = 4
+3 x + 2 y = 4
----------------- add
4 y = 8
y = 2
then
3 x + 4 = 4
x = 0
so they intersect at
(0,2)
To create a linear system with exactly one solution, we need to ensure that the two equations are not parallel, meaning their slopes are not equal.
The given equation is -3x + 2y = 4. To find another equation that forms a system with exactly one solution, we can manipulate the given equation to change its slope while still keeping the relationship between x and y proportional.
Let's start by getting the equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
-3x + 2y = 4
2y = 3x + 4 (Adding 3x to both sides)
y = (3x + 4) / 2 (Dividing both sides by 2)
Now, we have the equation in slope-intercept form. To create another equation, we can modify the slope (m). Let's choose a different slope, such as 2.
y = 2x + b
To determine the value of b, we can use the fact that the new equation should intersect the given equation at exactly one point. We can substitute the x and y values from the first equation into the second equation and solve for b.
Substituting x = 0, y = 2 into the second equation:
2 = 2(0) + b
2 = b
So, the second linear equation that forms a system with exactly one solution is: y = 2x + 2.