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
91 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 is the smallest positive integer solution to the equation a^n + b^n = c^n for n > 2, as stated in Fermat's Last Theorem?
+
Math Question: What is the value of log(base 3) 9 + log(base 2) 8?
+
What is the sum of 77 and 98?
+
New questions in Mathematics
find the value of the tangent if it is known that the cos@= 1 2 and the sine is negative. must perform procedures.
-x+3x-2,si x=3
Let X be a discrete random variable with range {1, 3, 5} and whose probability function is f(x) = P(X = x). If it is known that P(X = 1) = 0.1 and P(X = 3) = 0.3. What is the value of P(X = 5)?
A person who weighs 200 pounds on earth would weigh about 32 pounds on the moon. Find the weight of a person on earth who would weigh 15 pounds on the moon.
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?
224 × (6÷8)
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?
According to a survey in a country 27% of adults do not own a credit card suppose a simple random sample of 800 adults is obtained . Describe the sampling distribution of P hat , the sample proportion of adults who do not own a credit card
Two business partners have a bank balance of $17,942.00. After the first year their interest brings their balance to $18,928.91. What rate of interest is earned?
The ninth term of a given geometric progression, with reason q , is 1792, and its fourth term is 56. Thus, calculate the fourth term of another geometric progression, whose ratio is q +1 and whose first term is equal to the first term of the first P.G. described.
Exercise 1 An ejidal association wishes to determine the distribution for the three different crops that it can plant for the next season on its available 900 hectares. Information on the total available and how many resources are required for each hectare of cultivation is shown in the following tables: Total available resource Water 15,000 m3 Fertilizer 5,000 kg Labor 125 day laborers Requirements per cultivated hectare Corn Soybeans Wheat Water 15 25 20 Fertilizer 5 8 7 Labor** 1/8 1/5 1/4 *The data in fraction means that with one day laborer it will be possible to care for 8, 5 and 4 hectares respectively. * Sales of crops 1 and 3, according to information from the Department of Agriculture, are guaranteed and exceed the capacity of the cooperative. However, soybeans must be limited to a maximum of 150 hectares. On the other hand, the profits for each hectare of crop obtained are estimated at: $7,500 for corn, $8,500 for soybeans and $8,000 for wheat. The objectives are to determine: • How many hectares of each crop must be allocated so that the profit is maximum. R= • The estimated profits for the ejidal cooperative in the next growing season. R=
The points (-5,-4) and (3,6) are the ends of the diameter of the circle calculate subequation
3+7
Jasminder has made 55% of the recipes in a particular cookbook. If there are 9 recipes that he has never made, how many recipes does the cookbook contain?
Let X be a discrete random variable such that E(X)=3 and V(X)=5. Let 𝑌 = 2𝑋^2 − 3𝑋. Determine E(Y).
Total Users with an active Wise account = Total Active Users + Total Users who haven’t transacted Total Active Users = Total MCA Users + Total Send Users = Total New Users + Retained Users Total New Users = New Send Users + New MCA Users Total MCA Users = New MCA Users + Retained Users who transacted this month via MCA Total Send Users = New Send Users + Retained Users who transacted this month via Send Send CR = Total Send Users / Total Users with an active Wise account MCA CR = Total MCA Users / Total Users with an active Wise account New Send CR = New Send Users / New Profiles Created in Month New MCA CR = New MCA Users / New Profiles Created in Month We have recently witnessed a drop in MCA conversion, but send user conversion is stable, can you help explain why?
Given the word WEIRD, determine a four-letter offspring that can be formed with the letters of the word written above
A factory produces glass for windows. The thickness X of an arbitrarily selected pane of glass is assumed to be Normally distributed with expectation μ = 4.10 and standard deviation σ = 0.04. Expectation and Standard deviation is measured in millimeters. What is the probability that an arbitrary route has a thickness less than 4.00 mm?
56 × 12 = 672. How should you adjust this answer 672 to determine 57 × 12? a) The answer increases by 1 b) The answer increases by 57 c) The answer increases by 56 d) The answer increases by 12
The car with an irresponsible driver starts to brake when it goes through a red light. When passing the traffic light, he does so at a speed of 115 kph in the right lane. Further ahead, 70 meters from the traffic light, a child is crossing the street and falls. If the effect of the car's brakes is equivalent to a deceleration of magnitude 5.7m/s². Is the child hit by the car or not? How far from the traffic light does the car stop?