Can someone show me how to answer these questions step-by-step? Thanks!
Solve the equation for y in terms of x
1.2x + 7= y
2. x- 2/3y= 3
3.-12x + 3y = 48
Give any three ordered pairs that are solutions of the equation
4. -1/4y - x =0
5. 5x - y= -5
-MC
to solve for y in terms of y just set the equation equal to y. Then divide everything by the coefficiant of y.
#1) 2x+7=y (already correct)
#2) x-(2/3)y=3
x-3=(2/3)y (move y by itself)
(x-3)/(2/3)=y (divide by 2/3)
-->(3x-9)/2=y (simplify)
-12x + 3y = 48
add 12x to both sides
3y = 12x + 48
divide all terms by 3
y = 4x + 16
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-1/4y - x = 0
start as above: solve for y
add x to both sides
-1/4y = x
multiply all terms by -4
y = -4x
Now plug in 3 values for x (such as -1, 0, and 1) and find the value for y for each. The three resulting (x,y) pairs are ordered pairs.
Certainly! Here's a step-by-step guide to solve each of the given equations and find solutions:
1. 1.2x + 7 = y
To solve for y, we need to isolate it on one side of the equation. Start by subtracting 7 from both sides:
1.2x + 7 - 7 = y - 7
This simplifies to:
1.2x = y - 7
Thus, the equation in terms of y becomes:
y = 1.2x - 7
2. x - (2/3)y = 3
We'll again isolate y on one side of the equation. Start by multiplying both sides by 3 to get rid of the fraction:
3(x - (2/3)y) = 3(3)
Simplifying gives:
3x - 2y = 9
Now, we want to isolate y, so subtract 3x from both sides:
3x - 2y - 3x = 9 - 3x
This simplifies to:
-2y = -3x + 9
Divide both sides by -2 to solve for y:
y = (3/2)x - 9/2
3. -12x + 3y = 48
Similar to the previous examples, we'll isolate y by moving terms around. Start by adding 12x to both sides:
-12x + 12x + 3y = 12x + 48
This simplifies to:
3y = 12x + 48
Now, divide both sides by 3 to solve for y:
y = 4x + 16
For questions 4 and 5, we are asked to provide three ordered pairs that satisfy the equation. To find these coordinates, we can choose any values for x, substitute them into the equations, and solve for y. Let's choose x = 0, 1, and -1 for simplicity.
4. -1/4y - x = 0
For x = 0:
-1/4y - 0 = 0
This simplifies to:
-1/4y = 0
Multiply both sides by -4:
y = 0
So, the ordered pair is (0, 0).
5. 5x - y = -5
For x = 0:
5(0) - y = -5
This simplifies to:
-y = -5
Multiply both sides by -1:
y = 5
The ordered pair is (0, 5).
For x = 1:
5(1) - y = -5
This simplifies to:
5 - y = -5
Subtract 5 from both sides:
-y = -10
Multiply both sides by -1:
y = 10
The ordered pair is (1, 10).
For x = -1:
5(-1) - y = -5
This becomes:
-5 - y = -5
Add 5 to both sides:
-y = 0
Multiply both sides by -1:
y = 0
The ordered pair is (-1, 0).
So, three ordered pairs that satisfy the equation are: (0, 0), (1, 10), and (-1, 0).
I hope this guide helps! Let me know if you have any further questions.