1/2x-3/4y=-3-1/2; find value of x
2x-3=x-3y-1; find valud of y
1. graph
2. solve by substitution
This is the second time I have seen your question.
I did not answer it the first time since I could not decide what you meant.
1. Is it (1/2)x ... or is it 1/(2x)...
2. why would they have 3-1/2 on the right side? Is there a variable missing?
3. are you solving the first for x in terms of y??
4. in the second, are you solving for y in terms of x?
5. For their graphs, both would be straight lines that intersect, their intersection point is the solution to the system
6. I would solve the second equation for x, then sub that back into the first.
In reply to your questions:
1. It is (1/2)x
2. It is -3-1/2
3. Yes
4. Yes
To find the value of x in the equation 1/2x - 3/4y = -3 - 1/2, we can follow the steps.
1. Graph:
To graph the equation, we need to rearrange it into the standard form of a linear equation, which is in the form of y = mx + b.
1/2x - 3/4y = -3 - 1/2
Multiply every term by 4 to get rid of the fractions:
4 * (1/2x) - 4 * (3/4y) = 4 * (-3 - 1/2)
2x - 3y = -12 - 2
Now, rearrange the equation to make y the subject:
2x - 3y = -14
-3y = -2x - 14
Divide every term by -3 to isolate y:
y = (-2/3)x + 14/3
Now we can plot this equation on a graph.
2. Solve by substitution:
Given equation: 1/2x - 3/4y = -3 - 1/2
Step 1: Solve for x in terms of y:
1/2x = -3 - 1/2 + 3/4y
x = (-6 - 1 + 3y/2) / (1/2)
x = (-7 + 3y/2) / (1/2)
x = (-7 + 3y/2) * 2
x = -14 + 3y
Step 2: Substitute the value of x from Step 1 into the second equation: 2x - 3 = x - 3y - 1
2(-14 + 3y) - 3 = (-14 + 3y) - 3y - 1
-28 + 6y - 3 = -14 + 3y - 3y - 1
-31 + 6y = -15
6y = -15 + 31
6y = 16
y = 16/6
y = 8/3
Therefore, the value of y is 8/3.
Note: The value of x depends on the value of y, so there isn't a single value for x.
To find the value of x in the equation 1/2x - 3/4y = -3 - 1/2, we can solve it using the substitution method:
Step 1: Isolate one variable in terms of the other in one of the equations. Let's isolate x in terms of y in the given equation:
1/2x - 3/4y = -3 - 1/2
1/2x = -3 - 1/2 + 3/4y
1/2x = -6/2 - 1/2 + 3/4y
1/2x = -7/2 + 3/4y
Step 2: Solve for x by multiplying both sides of the equation by 2 to get rid of the fraction:
2 * (1/2x) = 2 * (-7/2 + 3/4y)
x = -7 + 3/2y
So the value of x is -7 + 3/2y.
To find the value of y in the equation 2x - 3 = x - 3y - 1, we can solve it using the substitution method as well:
Step 1: Isolate one variable in terms of the other in one of the equations. Let's isolate y in terms of x in the given equation:
2x - 3 = x - 3y - 1
3y = -x + 2x - 3 + 1
3y = x - 2
y = (1/3)x - 2/3
So the value of y is (1/3)x - 2/3.
Now, depending on the given values or additional equations/values, you can substitute these expressions for x and y into the original equations to find their exact values.