Answer:
The first equation must be multiplied by -5 to eliminate x variable by addition
Step-by-step explanation:
4 x - 3 y = 1 (1)
5 x + 4 y = 9 (2)
If the second equation is multiplied by 4
5x+4y=9. ×4
We have,
20x+16y=36 (3)
The first equation should be multiplied by -5 to eliminate x variable by addition
4x-3y=1 × -5
We have
-20x+15y=-5 (4)
Add equation (3) and (4) to eliminate x variable
20x+16y=36
-20x+15y=-5
31y=31
Divide both sides by 31
y=1
Substitute y=1 into equation (1)
4 x - 3 y = 1
4x-3(1)=1
4x-3=1
4x=1+3
4x=4
Divide both sides by 4
x=1
To solve this system by substitution, we must substitute in the value we are given for x in terms of y (the first equation) into the second equation. This is modeled below:
x = -8y - 15
2x + 5y = -8
2 (-8y - 15) + 5y = -8
Now, we should solve this new equation for y. To begin, we should use the distributive property to get rid of the parentheses on the left side of the equation and begin the simplification process.
-16y - 30 + 5y = -8
Next, we can combine like terms on the left side of the equation by adding together the two terms that both contain the variable y.
-11y - 30 = -8
Next, we should add 30 to both sides in order to move all of the constant (number) terms to the left side of the equation.
-11y = 22
After that, we should divide both sides of the equation by -11 in order to get the variable y alone.
y = -2
Now, we can substitute our value for y back into one of our original equations (it doesn't matter which one you choose; they will yield the same answer).
x = -8y - 15
x = -8(-2) - 15
To simplify, we should following the order of operations outlined by PEMDAS and compute the multiplication and then the subtraction.
x = 16 - 15
x = 1
Therefore, the answer to the system is x = 1 and y = -2, or (1,-2) when written as an ordered pair.
Hope this helps!
Answer:
153 cups of butter
Step-by-step explanation:
1 pack=34 cups
1 pack(4.5 packs)=34 cups(4.5)
4.5 packs=153 cups of butter
