Give the equivalent linear function in standard form: (ax + by = c):
a.x=9-3y/-2
b.y=-4x+5/3
a.
- 3 y / - 2 = 3 y / 2 = ( 3 / 2 ) y
So :
x = 9 - 3 y / - 2 = 9 + ( 3 / 2 ) y
x = 9 + ( 3 / 2 ) y Subtract ( 3 / 2 ) y to both sides
x - ( 3 / 2 ) y = 9 + ( 3 / 2 ) y - ( 3 / 2 ) y
x - ( 3 / 2 ) y = 9
When you compare with :
a x + b y = c
you can see :
a = 1
b = - ( 3 / 2 )
c = 9
b.
y = - 4 x + 5 / 3 Add 4 x to both sides
y + 4 x = - 4 x + 5 + 4 x
y + 4 x = 5
4 x + y = 1
When you compare with :
a x + b y = c
you can see :
a = 4
b = 1
c = 1
Thank you so much :D
To find the linear functions in standard form, we need to simplify the given equations and rearrange them in the form ax + by = c.
Given equations:
a. x = (9 - 3y) / -2
b. y = (-4x + 5) / 3
Let's begin with equation (a).
a. x = (9 - 3y) / -2
First, let's apply the distributive property to the numerator on the right side of the equation:
x = 9 / -2 - (3y / -2)
Next, let's simplify the fractions:
x = -9/2 - (3/2)y
To make the equation in standard form, we need to eliminate the fractions. Multiply every term by 2 to clear the denominators:
2x = -9 - 3y
Rearrange the equation by moving all terms to the left side:
2x + 3y = -9
Now, let's move on to equation (b).
b. y = (-4x + 5) / 3
Multiply through by 3 to clear the denominator:
3y = -4x + 5
Rearrange the equation by moving all terms to the left side:
4x + 3y = 5
The equivalent linear functions in standard form are:
a. 2x + 3y = -9
b. 4x + 3y = 5