given the equation -3x +2y =4, Write another equation that will form a linear system with:
one solution, no solution and infinite solution.
infinite solution:
(-3x +2y =) * 3 -> -9x +6y =12
y=3/2x+4
-9x +6y =12
I think we have to multiple the first equation by non-zero number right? But when I rewrite this -9x +6y =12 into slope-intercept form . it doesn't have to same answer as the original.
One Solution: Add to verify.
-3x + 2y = 4
3x + 2y = 4
No Solution: Multiply Eq1 by (-1) and add.
-3x + 2y = 4
-3x + 2y = 6
Infinite Solutions: Multiply Eq1 by 3 and compare.
-3x + 2y = 4
-9x + 6y = 12
To create another equation with an infinite solution, you need to multiply every term in the equation by the same non-zero number. In this case, you multiplied the equation -3x + 2y = 4 by 3, which gave you -9x + 6y = 12.
To check if this equation has an infinite solution, you can rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
By rearranging the equation -9x + 6y = 12, you can isolate y:
6y = 9x + 12
y = (9/6)x + 2
y = (3/2)x + 2
As you can see, when you rewrite the equation in slope-intercept form, you get y = (3/2)x + 2, which is different from the original equation y = (3/2)x + 4. This means that the system of equations -3x + 2y = 4 and -9x + 6y = 12 does not have an infinite solution but has a unique solution.