Find the slow of the graph of the following 9x-3y=15
To find the slope of the graph, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope.
Given equation: 9x - 3y = 15
Subtract 9x from both sides: -3y = -9x + 15
Divide all terms by -3: y = 3x - 5
Now we can observe that the equation is in the form y = mx + b, where m (slope) is 3.
Therefore, the slope of the graph is 3.
How many solutions does this system have?
X-2y=2
Y=-2x+5
To determine the number of solutions for this system of equations, we can solve them simultaneously and check if they intersect at a single point, are parallel lines, or coincide (represent the same line).
The system of equations is:
x - 2y = 2
y = -2x + 5
To solve it, we can substitute the second equation into the first equation:
x - 2(-2x + 5) = 2
x + 4x - 10 = 2
5x - 10 = 2
5x = 12
x = 12/5
Substituting this value of x into the second equation, we can find the corresponding y-value:
y = -2(12/5) + 5
y = -24/5 + 25/5
y = 1/5
Therefore, the solution to the system of equations is (12/5, 1/5) or x ≈ 2.4, y ≈ 0.2.
Since we have found a unique solution for this system, we can conclude that it has exactly one solution.
Solve the system by either substitution or elimination
3x-5y=21
2x+y=1
We can solve this system by substitution or elimination.
Method 1: Substitution
Step 1: Solve one of the equations for one variable in terms of the other variable.
We will solve the second equation for y.
2x + y = 1
y = 1 - 2x
Step 2: Substitute the expression for y into the other equation and solve for x.
3x - 5(1 - 2x) = 21
3x - 5 + 10x = 21
13x - 5 = 21
13x = 26
x = 2
Step 3: Substitute the value of x back into one of the original equations and solve for y.
2(2) + y = 1
4 + y = 1
y = -3
The solution to the system of equations is x = 2, y = -3.
Method 2: Elimination
Step 1: Multiply both sides of the second equation by 5 to make the coefficients of y the same in both equations.
2x + y = 1
10x + 5y = 5
Step 2: Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x the same in both equations.
(5)(3x - 5y) = (5)(21)
15x - 25y = 105
(3)(2x + y) = (3)(1)
6x + 3y = 3
Step 3: Add the equations together to eliminate x.
15x - 25y + 6x + 3y = 105 + 3
21x - 22y = 108
Step 4: Solve the resulting equation for y.
21x - 22y = 108
-22y = 108 - 21x
y = (108 - 21x)/-22
Step 5: Substitute the expression for y back into one of the original equations and solve for x.
3x - 5[(108 - 21x)/-22] = 21
66x + 110 - 105x = -231
66x - 105x = -231 - 110
-39x = -341
x = 341/39
x = 341/39
Step 6: Substitute the value of x back into one of the original equations and solve for y.
2(341/39) + y = 1
(682/39) + y = 1
y = 1 - (682/39)
y = (39 - 682)/39
y = -643/39
The solution to the system of equations is x = 341/39, y = -643/39, which can be simplified to approximately x ≈ 8.74, y ≈ -16.49.
To find the slope of the graph represented by the equation 9x - 3y = 15, we need to rearrange the equation into slope-intercept form, which is y = mx + b. In this form, m represents the slope of the line.
Let's rearrange the equation:
9x - 3y = 15
First, subtract 9x from both sides:
-3y = -9x + 15
Next, divide both sides by -3 to isolate y:
y = (9/3)x - 15/3
Simplifying further:
y = 3x - 5
Now we can see that the equation is in slope-intercept form, y = mx + b, where m is the coefficient of x. In this case, the slope of the graph is 3.
To find the slope of the graph represented by the equation 9x - 3y = 15, we need to rewrite the equation in slope-intercept form (y = mx + b), where m is the slope.
Let's begin by isolating y in the equation:
9x - 3y = 15
First, we'll subtract 9x from both sides:
-3y = -9x + 15
Now, divide both sides by -3 to solve for y:
y = (9/3)x - 5
The equation is now in slope-intercept form, where the coefficient of x (9/3) represents the slope. Simplifying further, we have:
y = 3x - 5
Therefore, the slope of the graph represented by the equation 9x - 3y = 15 is 3.