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:
1.) r>-3/4 and 2.) 157<-1
Answer:
(2, 1)
Step-by-step explanation:
The best way to do this to avoid tedious fractions is to use the addition method (sometimes called the elimination method). We will work to eliminate one of the variables. Since the y values are smaller, let's work to get rid of those. That means we have to have a positive and a negative of the same number so they cancel each other out. We have a 2y and a 3y. The LCM of those numbers is 6, so we will multiply the first equation by a 3 and the second one by a 2. BUT they have to cancel out, so one of those multipliers will have to be negative. I made the 2 negative. Multiplying in the 3 and the -2:
3(-9x + 2y = -16)--> -27x + 6y = -48
-2(19x + 3y = 41)--> -38x - 6y = -82
Now you can see that the 6y and the -6y cancel each other out, leaving us to do the addition of what's left:
-65x = -130 so
x = 2
Now we will go back to either one of the original equations and sub in a 2 for x to solve for y:
19(2) + 3y = 41 so
38 + 3y = 41 and
3y = 3. Therefore,
y = 1
The solution set then is (2, 1)
Answer:
Step-by-step explanation:
convert mixed fractions to improper fractions
rule=a b/c=(ac+b)/c
(1 1/3)/(1 3/4)
(4/3)/(7/4)
rule for dividing fractions=(a/b)/(c/d)=(a/b)(d/c)
(4/3)(4/7) then you can multiply the numerators and denominators
16/21
