Question

Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2

127

likes
635 views

Answer to a math question Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2

Expert avatar
Santino
4.5
111 Answers
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
0.01x-0.08y=0.1,0.2x+0.6y=0.2
To make $\frac{x}{100}$ and $\frac{x}{5}$ equal, multiply all terms on each side of the first equation by $0.2$ and all terms on each side of the second by $0.01$.
0.2\times 0.01x+0.2\left(-0.08\right)y=0.2\times 0.1,0.01\times 0.2x+0.01\times 0.6y=0.01\times 0.2
Simplify.
0.002x-0.016y=0.02,0.002x+0.006y=0.002
Subtract $0.002x+0.006y=0.002$ from $0.002x-0.016y=0.02$ by subtracting like terms on each side of the equal sign.
0.002x-0.002x-0.016y-0.006y=0.02-0.002
Add $\frac{x}{500}$ to $-\frac{x}{500}$. Terms $\frac{x}{500}$ and $-\frac{x}{500}$ cancel out, leaving an equation with only one variable that can be solved.
-0.016y-0.006y=0.02-0.002
Add $-\frac{2y}{125}$ to $-\frac{3y}{500}$.
-0.022y=0.02-0.002
Add $0.02$ to $-0.002$ by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
-0.022y=0.018
Divide both sides of the equation by $-0.022$, which is the same as multiplying both sides by the reciprocal of the fraction.
y=-\frac{9}{11}
Substitute $-\frac{9}{11}$ for $y$ in $0.2x+0.6y=0.2$. Because the resulting equation contains only one variable, you can solve for $x$ directly.
0.2x+0.6\left(-\frac{9}{11}\right)=0.2
Multiply $0.6$ times $-\frac{9}{11}$ by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.
0.2x-\frac{27}{55}=0.2
Add $\frac{27}{55}$ to both sides of the equation.
0.2x=\frac{38}{55}
Multiply both sides by $5$.
x=\frac{38}{11}
The system is now solved.
x=\frac{38}{11},y=-\frac{9}{11}

Frequently asked questions (FAQs)
What are the two key characteristics of the tangent function f(x) = tan(x)? Also, determine the value of f(π/4).
+
How many diagonals are there in a 12-sided polygon of any type?
+
Math question: Convert 3.45 x 10^6 to standard notation.
+
New questions in Mathematics
The strength of Kefexin oral suspension is 100 mg/ml. Nora has been prescribed cefalexin at a dose of 50 mg/kg/day divided in two single doses. Nora weighs 14 kg. How many milliliters of solution for Nora should be given as a single dose?
A software company incurs a cost of $50 per license sold plus $5,000 in fixed costs. How many licenses should you sell to minimize total costs?
A circular park has a diameter of 150ft. A circular fence is to be placed on the edge of this park. Calculate the cost of fencing this park if the rate charged is $7 per foot. Use π = 3.14.
11(4x-9)= -319
(x^2+3x)/(x^2-9)=
How many kilometers does a person travel in 45 minutes if they move at a rate of 8.3 m/s?
(5-(4-3)*3)-(8+5))
Let I ⊂ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≤ b and I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)
All the liquid contained in a barrel is distributed into 96 equal glasses up to its maximum capacity. We want to pour the same amount of liquid from another barrel identical to the previous one into glasses identical to those used, but only up to 3/4 of its capacity. How many more glasses will be needed for this?
Answer the following questions regarding the expression below. 0.1 (a) Write the number as a fraction.
We have spent 1/4 of the inheritance on taxes and 3/5 of the rest on buying a house. If the inheritance was a total of €150,000 How much money do we have left?
A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?
I want you to solve this problem as a grade sixth pupil in primary school: 8 Pigs ate 6 bags of fee in 20 days. How long will it take 10 pigs to eat 15 bags of feed eating at the same rate?
You want to study incomes in a large city. You take a simple random sample of 5012 households and find that the distribution of household incomes is skewed right. If you calculate the mean of the 5012 household incomes will the distribution of mean scores be skewed right as well? Hint: this involves the Central Limit Theorem.
How to convert 45 kg into grams
7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?
Salut👋🏻 Appuie sur "Créer une nouvelle tâche" pour envoyer ton problème de mathématiques. Un de nos experts commencera à travailler dessus immédiatement !
To paint a 250 m wall, a number of workers were employed. If the wall were 30 m longer, 9 more workers would be needed. How many were employed at the beginning?
answer this math question The scale on a map is drawn so that 5.5 inches corresponds to an actual distance of 225 miles. If two cities are 12.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) miles apart. The two cities are how many miles apart
If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. Round answer to 2 decimal places and enter the units.