{3x-2y=10
{-1.5x+y=5
these are part of the same question i was wondering how the heck i solve this i have been stuck on this for hours and keeping getting dead ends and i cant you a graph.
since -1.5x + y = 5,
y = 1.5x + 5
Now substitute that into the 1st equation and you have
3x - 2(1.5x+5) = 10
3x - 3x - 10 = 10
-10 = 10
There is no solution to this. Thus, there are no solutions to the pair of equations.
Another way to look at is to note that if you miltiply the 2nd equation by -2, it becomes
3x - 2y = -10
But the first equation says that 3x-2y = 10
There is no way that 3x-2y can be both 10 and -10
so wait would i just use the X and Y from 3x-2y=10?
OOOOOOOOOOOO wait i just got it nvm THANKS!!
good. The two lines are parallel, so they never meet. Thus, there is no intersection which could be the solution to both equations.
To solve this system of equations without using a graph, you can use a method called elimination or substitution. Let's go through both methods step by step:
Method 1: Elimination
1. Multiply the second equation by 2 to make the coefficient of 'y' the same as in the first equation.
-1.5x + y = 5 Multiply both sides by 2
-3x + 2y = 10
2. Now we have:
3x - 2y = 10 (Equation 1)
-3x + 2y = 10 (Equation 2)
3. Add Equation 1 and Equation 2 together. This will eliminate the 'x' terms.
(3x - 2y) + (-3x + 2y) = 10 + 10
0 = 20
4. Since 0 = 20 is not a true statement, this means the system of equations is inconsistent. There is no solution.
Method 2: Substitution
1. Solve one equation for one variable. Let's solve the second equation for 'y':
-1.5x + y = 5 (Equation 2)
y = 1.5x + 5
2. Substitute the value of 'y' from Equation 2 into Equation 1:
3x - 2(1.5x + 5) = 10
3. Simplify and solve for 'x':
3x - 3x - 10 = 10
-10 = 10
4. Since -10 = 10 is not a true statement, this means the system of equations is inconsistent. There is no solution.
In conclusion, the given system of equations has no solution. This means that the lines represented by the equations are parallel.