The solution to
�
=
1
2
�
+
2
y=
2
1
x+2 and
�
=
−
1
4
�
+
8
y=−
4
1
x+8 is
23 answers
There is not a unique solution to this system of equations. It represents two parallel lines that do not intersect. Thus, there are no values of x and y that satisfy both equations simultaneously.
y =1/2x+2and y= -1/4x+8
To find the solution to this system of equations, you can set the two equations equal to each other:
1/2x + 2 = -1/4x + 8
To eliminate the fractions, you can multiply both sides of the equation by the least common multiple of the denominators, which is 4:
4(1/2x + 2) = 4(-1/4x + 8)
2x + 8 = -x + 32
Now, you can combine like terms:
2x + x = 32 - 8
3x = 24
Dividing both sides by 3:
x = 8
Now that you have the value of x, you can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
y = 1/2(8) + 2
y = 4 + 2
y = 6
Therefore, the solution to the system of equations is x = 8 and y = 6.
1/2x + 2 = -1/4x + 8
To eliminate the fractions, you can multiply both sides of the equation by the least common multiple of the denominators, which is 4:
4(1/2x + 2) = 4(-1/4x + 8)
2x + 8 = -x + 32
Now, you can combine like terms:
2x + x = 32 - 8
3x = 24
Dividing both sides by 3:
x = 8
Now that you have the value of x, you can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
y = 1/2(8) + 2
y = 4 + 2
y = 6
Therefore, the solution to the system of equations is x = 8 and y = 6.
The solution to y=3 and x=-1
The solution to the equations y = 3 and x = -1 is x = -1 and y = 3.
Graph and then find the solution for y=3 and x=-1
To graph the equation y = 3, we can plot a single point on the y-axis at y = 3. Similarly, for x = -1, we plot a single point on the x-axis at x = -1. The solution to the system of equations is the point where the two graphs intersect.
Here is a graph showing the equation y = 3 plotted as a horizontal line at y = 3 and x = -1 plotted as a point on the x-axis:
```
| .
3 |______________________
| |
| |
| |
| |
| |
0|______________________
-1
```
As you can see, the point (-1, 3) represents the solution to the system of equations y = 3 and x = -1.
Here is a graph showing the equation y = 3 plotted as a horizontal line at y = 3 and x = -1 plotted as a point on the x-axis:
```
| .
3 |______________________
| |
| |
| |
| |
| |
0|______________________
-1
```
As you can see, the point (-1, 3) represents the solution to the system of equations y = 3 and x = -1.
The solution to y=-1/2x-6 and y=7/6x+4
To find the solution to the system of equations y = -1/2x - 6 and y = 7/6x + 4, we can set the two equations equal to each other:
-1/2x - 6 = 7/6x + 4
To eliminate the fractions, we can multiply both sides of the equation by the least common multiple of the denominators, which is 6:
6(-1/2x - 6) = 6(7/6x + 4)
-3x - 36 = 7x + 24
To isolate the variable x, we can combine like terms by adding 3x to both sides and subtracting 24 from both sides:
-3x - 7x = 24 + 36
-10x = 60
Dividing both sides by -10:
x = -6
Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
y = -1/2(-6) - 6
y = 3 - 6
y = -3
Therefore, the solution to the system of equations is x = -6 and y = -3.
-1/2x - 6 = 7/6x + 4
To eliminate the fractions, we can multiply both sides of the equation by the least common multiple of the denominators, which is 6:
6(-1/2x - 6) = 6(7/6x + 4)
-3x - 36 = 7x + 24
To isolate the variable x, we can combine like terms by adding 3x to both sides and subtracting 24 from both sides:
-3x - 7x = 24 + 36
-10x = 60
Dividing both sides by -10:
x = -6
Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
y = -1/2(-6) - 6
y = 3 - 6
y = -3
Therefore, the solution to the system of equations is x = -6 and y = -3.
8x+2y=25
To find the solution to the equation 8x + 2y = 25, we can choose values for x and solve for y, or vice versa.
Let's solve for y when x = 0:
8(0) + 2y = 25
0 + 2y = 25
2y = 25
y = 25/2
y = 12.5
So one solution to the equation is when x = 0 and y = 12.5.
Now let's solve for x when y = 0:
8x + 2(0) = 25
8x + 0 = 25
8x = 25
x = 25/8
So another solution to the equation is when x = 25/8 and y = 0.
Therefore, the solution to the equation 8x + 2y = 25 is (0, 12.5) and (25/8, 0).
Let's solve for y when x = 0:
8(0) + 2y = 25
0 + 2y = 25
2y = 25
y = 25/2
y = 12.5
So one solution to the equation is when x = 0 and y = 12.5.
Now let's solve for x when y = 0:
8x + 2(0) = 25
8x + 0 = 25
8x = 25
x = 25/8
So another solution to the equation is when x = 25/8 and y = 0.
Therefore, the solution to the equation 8x + 2y = 25 is (0, 12.5) and (25/8, 0).
Find the slope and y-intercept that has infinite solutions to the equation Click Here for Help Video
8
�
+
2
�
=
25
8x+2y=25
The slope would be
.
The y-intercept would be
. (Do not list as a coordinate point.)
8
�
+
2
�
=
25
8x+2y=25
The slope would be
.
The y-intercept would be
. (Do not list as a coordinate point.)
To find the slope and y-intercept of the equation 8x + 2y = 25, we can rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To convert the equation into slope-intercept form, we need to isolate y on one side:
8x + 2y = 25
Subtract 8x from both sides:
2y = -8x + 25
Now divide both sides by 2:
y = -4x + 12.5
The equation y = -4x + 12.5 is in slope-intercept form.
The slope of the equation is -4.
The y-intercept of the equation is 12.5.
To convert the equation into slope-intercept form, we need to isolate y on one side:
8x + 2y = 25
Subtract 8x from both sides:
2y = -8x + 25
Now divide both sides by 2:
y = -4x + 12.5
The equation y = -4x + 12.5 is in slope-intercept form.
The slope of the equation is -4.
The y-intercept of the equation is 12.5.
Find the slope and y-intercept that has infinite solutions to the equation Click Here for Help Video
−
6
�
+
2
�
=
36
−6x+2y=36
The slope would be
.
The y-intercept would be
. (Do not list as a coordinate point.)
−
6
�
+
2
�
=
36
−6x+2y=36
The slope would be
.
The y-intercept would be
. (Do not list as a coordinate point.)
To find the slope and y-intercept of the equation -6x + 2y = 36, we can rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To convert the equation into slope-intercept form, we need to isolate y on one side:
-6x + 2y = 36
Add 6x to both sides:
2y = 6x + 36
Now divide both sides by 2:
y = 3x + 18
The equation y = 3x + 18 is in slope-intercept form.
The slope of the equation is 3.
The y-intercept of the equation is 18.
To convert the equation into slope-intercept form, we need to isolate y on one side:
-6x + 2y = 36
Add 6x to both sides:
2y = 6x + 36
Now divide both sides by 2:
y = 3x + 18
The equation y = 3x + 18 is in slope-intercept form.
The slope of the equation is 3.
The y-intercept of the equation is 18.
Solve the following inequality. Click Here for help Video
−
10
6
�
≤
4
6
−10
y ≤4
�
y
−
10
6
�
≤
4
6
−10
y ≤4
�
y
The solution to the inequality -10/6y ≤ 4 is y ≤ 4/(-10/6).
To simplify the expression, we can multiply the numerator and denominator of 4/(-10/6) by 6 to get:
y ≤ (4 * 6) / (-10)
Simplifying further, we have:
y ≤ 24 / (-10)
y ≤ -12/5
Therefore, the solution to the inequality -10/6y ≤ 4 is y ≤ -12/5.
To simplify the expression, we can multiply the numerator and denominator of 4/(-10/6) by 6 to get:
y ≤ (4 * 6) / (-10)
Simplifying further, we have:
y ≤ 24 / (-10)
y ≤ -12/5
Therefore, the solution to the inequality -10/6y ≤ 4 is y ≤ -12/5.
Solve the following inequality. Click Here for help Video
−
10
(
−
10
�
+
10
)
≤
10
−10(−10x+10)≤10
�
x
−
10
(
−
10
�
+
10
)
≤
10
−10(−10x+10)≤10
�
x
To solve the inequality -10(-10x+10) ≤ 10, we can simplify the expression by distributing -10 to the terms inside the parentheses:
100x - 100 ≤ 10
Next, we can add 100 to both sides of the inequality to isolate the variable:
100x ≤ 10 + 100
100x ≤ 110
Finally, we divide both sides of the inequality by 100 to solve for x:
x ≤ 110/100
Simplifying further, we have:
x ≤ 11/10
Therefore, the solution to the inequality -10(-10x+10) ≤ 10 is x ≤ 11/10.
100x - 100 ≤ 10
Next, we can add 100 to both sides of the inequality to isolate the variable:
100x ≤ 10 + 100
100x ≤ 110
Finally, we divide both sides of the inequality by 100 to solve for x:
x ≤ 110/100
Simplifying further, we have:
x ≤ 11/10
Therefore, the solution to the inequality -10(-10x+10) ≤ 10 is x ≤ 11/10.
Solve the following inequalities. Click Here for Help Video
5
�
<
20
5x<20
�
x
−
5
�
<
20
−5y<20
�
y
5
�
<
−
20
5z<−20
�
z
5
�
<
20
5x<20
�
x
−
5
�
<
20
−5y<20
�
y
5
�
<
−
20
5z<−20
�
z
To solve the inequality 5x < 20, we can divide both sides of the inequality by 5:
x < 20/5
Simplifying further, we have:
x < 4
Therefore, the solution to the inequality 5x < 20 is x < 4.
To solve the inequality -5y < 20, we can divide both sides of the inequality by -5. However, dividing by a negative number requires flipping the direction of the inequality:
y > 20/(-5)
Simplifying further, we have:
y > -4
Therefore, the solution to the inequality -5y < 20 is y > -4.
To solve the inequality 5z < -20, we can divide both sides of the inequality by 5:
z < -20/5
Simplifying further, we have:
z < -4
Therefore, the solution to the inequality 5z < -20 is z < -4.
x < 20/5
Simplifying further, we have:
x < 4
Therefore, the solution to the inequality 5x < 20 is x < 4.
To solve the inequality -5y < 20, we can divide both sides of the inequality by -5. However, dividing by a negative number requires flipping the direction of the inequality:
y > 20/(-5)
Simplifying further, we have:
y > -4
Therefore, the solution to the inequality -5y < 20 is y > -4.
To solve the inequality 5z < -20, we can divide both sides of the inequality by 5:
z < -20/5
Simplifying further, we have:
z < -4
Therefore, the solution to the inequality 5z < -20 is z < -4.
Solve the following inequalities
5z<−20
�
z
5z<−20
�
z
To solve the inequality 5z < -20, we can divide both sides of the inequality by 5:
z < -20/5
Simplifying further, we have:
z < -4
Therefore, the solution to the inequality 5z < -20 is z < -4.
z < -20/5
Simplifying further, we have:
z < -4
Therefore, the solution to the inequality 5z < -20 is z < -4.
9 answers