solve the system. Give the x-value of the solution.
3x-5y=16 and -9x+15=48
answer key:
7
0
no solution
infinite number solution
3x-5y=16
-9x+15=48
notice that if you divide the 2nd by -3 , you get
3x - 5y = -16
clearly you will have two different parallel lines, thus no solution.
or
if we subtract:
3x-5y=16
3x-5y=-16
0 = 32
not very likely !!!! , so no solution
To solve the given system of equations, we will use the method of substitution.
1. Start by isolating one variable in one of the equations. Let's solve the second equation for x:
-9x + 15 = 48
Subtract 15 from both sides:
-9x = 33
Divide both sides by -9:
x = -33/9
Simplify:
x = -11/3
2. Now that we have the value of x, we substitute it into one of the equations to find the value of y. Let's use the first equation:
3x - 5y = 16
Substitute x = -11/3:
3(-11/3) - 5y = 16
Simplify:
-11 - 5y = 16
Add 11 to both sides:
-5y = 27
Divide both sides by -5:
y = -27/5
Simplify:
y = -5.4
So, the solution to the system of equations is x = -11/3 and y = -27/5.
Now, let's determine the x-value of the solution:
The x-value of the solution refers to the value of x when y is not considered. It means we are looking for the x-coordinate of the point where the two lines intersect on the x-axis.
In this case, the x-coordinate of the solution is -11/3. So, the x-value of the solution is -11/3 or approximately -3.67.
Therefore, the x-value of the solution is -3.67.
Note: If the system of equations has no solution or an infinite number of solutions, the x-value of the solution cannot be determined. In such cases, the x-value may be represented as "no solution" or "infinite number of solutions."