$MathMaster logo$

MathMaster

Home
general
given two lines l1 x 4y 10 and l2 2x y 7 i find the intersection point of l1 and l2

Question

Given two lines 𝐿1: 𝑥 + 4𝑦 = −10 and 𝐿2: 2𝑥 − 𝑦 = 7. i. Find the intersection point of 𝐿1 and 𝐿2.

68

likes

340 views

Answer to a math question Given two lines 𝐿1: 𝑥 + 4𝑦 = −10 and 𝐿2: 2𝑥 − 𝑦 = 7. i. Find the intersection point of 𝐿1 and 𝐿2.

$Expert avatar$

4.5

93 Answers

To find the intersection point of two lines, we need to solve the system of equations formed by the equations of the lines.

Given:
Line L1: x + 4y = -10
Line L2: 2x - y = 7

We can solve this system of equations by using any method like substitution, elimination, or matrices. Let's solve it using the substitution method.

Step 1: Solve one equation for one variable in terms of the other variable.
From the equation of L2, we can isolate y:
y = 2x - 7.

Step 2: Substitute the expression for the variable in the other equation.
Substitute y with (2x - 7) in the equation of L1:
x + 4(2x - 7) = -10.

Step 3: Simplify and solve for the remaining variable.
x + 8x - 28 = -10
9x - 28 = -10
9x = 18
x = 2.

Step 4: Substitute the value of x back into one of the original equations to find the value of y.
Using L2: 2(2) - y = 7
4 - y = 7
-y = 7 - 4
-y = 3
y = -3.

Therefore, the intersection point of L1 and L2 is (2, -3).

Answer: The intersection point of L1 and L2 is

(2, -3)

.

Frequently asked questions (FAQs)

What is the result of dividing 84 by 7 and then adding 5 to the quotient?

+

What is the probability of rolling a fair six-sided die and getting an odd number?

+

What is the value of 'a' in the parabola function 𝑦 = ax^2 if the vertex is (-2, 5) and it passes through the point (1, 2)?

+

New questions in Mathematics

8x²-30x-10x²+70x=-30x+10x²-20x²

What payment 7 months from now would be equivalent in value to a $3,300 payment due 23 months from now? The value of money is 2.7% simple interest. Round your answer to 2 decimal places. Show all work and how you arrive at the answer..

If L (-2, -5) reflected across y = -4. What are the coordinates of L?

How many different ways can a psychology student select 5 subjects from a pool of 20 subjects and assign each one to a different experiment?

The durability of a tire of a certain brand is a Normal random variable with an average of 64,000 km and a standard deviation of 9,000 km. Assuming independence between tires, what is the probability that the 4 tires on a car will last more than 58,000 km?

The thermal representation f(x) = 20 times 0.8 to the power of x is known from an exponential function f. Specify the intersection point with the y-axis

reduce the expression (7.5x 12)÷0.3

User Before the election, a poll of 60 voters found the proportion who support the Green candidate to be 25%. Calculate the 90% confidence interval for the population parameter. (Give your answers as a PERCENTAGE rounded to TWO DECIMAL PLACES: exclude any trailing zeros and DO NOT INSERT THE % SIGN) Give the lower limit of the 90% confidence interval Give the upper limit of the 90% confidence interval

Shows two blocks, masses 4.3 kg and 5.4 kg, being pushed across a frictionless surface by a 22.5-N horizontal force applied to the 4.3-kg block. A. What is the acceleration of the blocks? B. What is the force of the 4.3-kg block on the 5.4 -kg block? C. What is the force of the 5.4 -kg block on the 4.3 -kg block?

The simple average of 15 , 30 , 40 , and 45 is

cube root of 56

A hardware bill totals $857.63 with discounts of 5% and 3%. What is the net cost of the Material ?

Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.

How to convert 45 kg into grams

How to factorise 5y^2 -7y -52

Find the set of points formed by the expression 𝜋<|𝑧−4+2𝑖|<3𝜋.

-Please answer to the following questions: What is the price elasticity of demand? Can you explain it in your own words? What is the price elasticity of supply? Can you explain it in your own words? What is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that? B-Assume that the supply of low-skilled workers is fairly elastic, but the employers’ demand for such workers is fairly inelastic. If the policy goal is to expand employment for low-skilled workers, is it better to focus on policy tools to shift the supply of unskilled labor or on tools to shift the demand for unskilled labor? What if the policy goal is to raise wages for this group? Explain your answers with supply and demand diagrams. Make sure to properly cite and reference your academic or peer-reviewed sources (minimum 2).

Exercise The temperature T in degrees Celsius of a chemical reaction is given as a function of time t, expressed in minutes, by the function defined on ¿ by: T (t )=(20 t +10)e−0.5t. 1) What is the initial temperature? 2) Show that T' (t )=(−10 t +15)e−0 .5t. 3) Study the sign of T' (t ), then draw up the table of variations of T . We do not ask for the limit of T in +∞. 4) What is the maximum temperature reached by the reaction chemical. We will give an approximate value to within 10−2. 5) After how long does the temperature T go back down to its initial value? We will give an approximate value of this time in minutes and seconds. DM 2: study of a function Exercise The temperature T in degrees Celsius of a chemical reaction is given as a function of time t, expressed in minutes, by the function defined on ¿ by: T (t )=(20 t +10)e−0.5t. 1) What is the initial temperature? 2) Show that T' (t )=(−10 t +15)e−0.5 t. 3) Study the sign of T' (t ), then draw up the table of variations of T . We do not ask for the limit of T in +∞. 4) What is the maximum temperature reached by the reaction chemical. We will give an approximate value to within 10−2. 5) After how long does the temperature T go back down to its initial value? We will give an approximate value of this time in minutes and seconds.