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2 years ago

2x - 3y = 9; 2x + y = 13

Mathematics

1 answer:

olga2289 [7]2 years ago

8 0

Answer:

See explanations below

Step-by-step explanation:

Given the simultaneous equations;

2x - 3y = 9... 1

2x + y = 13 ... 2

From 2;

y = 13-2x

Substitute into 1;

2x - 3(13-2x) = 9

2x -39 + 6x = 9

8x - 39 = 9

8x = 9+39

8x = 48

x = 6

Since y = 13-2x

y = 13-2(6)

y = 13-12

y = 1

The soluton to the system of equation is (6, 1)

Given the equations;

99x + 101y = 499; .... 1 * 101

101x + 99 y = 501 ... 2 * 99

______________

9999x + 10,201y = 50,399

9999x + 9801y = 49,599

Subtract

10201y - 9801y = 50399-49599

400y = 800

y = 2

Substitute y = 2 into 1;

From 1;

99x + 101y = 499

99x + 101(2) =499

99x +202 = 499

99x = 499 - 202

99x = 198

x = 198/99

x =2

Hence the solution is (2,2)

For the equations;

49x - 57y = 172 .... * 57

57x - 49y = 252 __ * 49

____________________

2793x -3249y = 9804

2793x - 2401y = 12348

Subtract

-3249y+2401y = 9804-12348

-848y = -2544

y = 3

Substitute into 1;

49x - 57y = 172

49x - 57(3) = 172

49x - 171 = 172

49x = 171+172

49x = 343

x = 7

Hence the solution is (7, 3)

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PLZ HELP STUCK ON THIS QUESTION 4a + 6b = 24 6a - 12b = -6 Given the equations what is the value of a+b? PLZ HELP WILL MARK BRAI

Paul [167]

Answer:

a + b = 5

Step-by-step explanation:

To solve this system of equations, we can use a strategy called elimination, which is when we get rid of a variable by adding/subtracting two equations.

Firstly, we want to make sure the absolute value of the coefficients that equal.

Lets eliminate b:

4a + 6b = 24

Multiply both sides by 2:

8a + 12b = 48

We also have:

6a - 12b = -6.

Now lets add that with

8a + 12b = 48

-> 6a + 8a + 12b - 12b = 48 -6

-> 14a = 42

-> a = 3

Now that we know a, lets plug it into one of our original equations:

4(3) + 6b = 24

12 + 6b = 24

6b = 12

b = 2

Finally, add the two values we found:

a+b = 2+3= 5

4 0

2 years ago

MO bisects angle LMN , angle LMO = 6x-22 and angle NMO = 2x +34. Solve for x and find angle LMN.

Mkey [24]

Answer:

$x=14$

$\angle{LMN}=124\textdegree$

Step-by-step explanation:

To Determine:

Solve for x and find angle LMN.

Fetching Information and Solution Steps:

Considering the angle $\angle{LMN}$

As MO bisects the angle $\angle{LMN}$ into two equal angle parts. These equal angles are:

$\angle{LMO}=6x-22$

$\angle{NMO}=2x+34$

As these angles are equal. i.e.

$\angle{LMO}=\angle{NMO}$

$6x-22=2x+34$

$\mathrm{Add\:}22\mathrm{\:to\:both\:sides}$

$6x-22+22=2x+34+22$

$6x=2x+56$

$\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}$

$6x-2x=2x+56-2x$

$4x=56$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\frac{4x}{4}=\frac{56}{4}$

$\mathrm{Simplify}$

$x=14$

Hence, $x=14$

As $\angle{LMN}$ was cut into two equal parts $\angle{LMO}$ and $\angle{NMO}$

So,

$\angle{LMN}$ = $\angle{LMO} + \angle{NMO}$

= $6x-22+2x+34$

= $8x + 12$

= $8(14) + 12$ ∵ $x=14$

= $124\textdegree$

Therefore, $\angle{LMN}=124\textdegree$

Keywords: angle bisector, congruent angles

Learn more about angle bisector and congruent angles from brainly.com/question/711370

#learnwithBrainly

3 0

3 years ago

Which point is not on the graph of y =2x + 3?

Nostrana [21]

Answer:

i'm pretty sure its D

Step-by-step explanation:

if you make a graph yourself you'll see all the rel;relationship match except for d

3 0

2 years ago

Find each percent decrease round to the nearest percent from 145 pounds to 132 pounds

BabaBlast [244]

9% decrease because 145-132=13
13=9% of 145

7 0

3 years ago

Read 2 more answers

The area of the triangle formed by points of intersection of parabola y=a(x−3)(x+2) with the coordinate axes is 10. Find a if it

ICE Princess25 [194]

Answer: a = 4

Step-by-step explanation: Area of a triangle is calculated as: $A_{t}=\frac{b.h}{2}$ .

The triangle formed by the parabola has base (b) equal to the distance between the points where the graph touches x-axis and height (h) is the point where graph touches the y-axis.

The points on the x-axis are the roots of the quadratic equation:

a(x-3)(x+2)=0

(x-3)(x+2)=0

x - 3 = 0

x = 3

x + 2 = 0

x = -2

So, base is the distance between (-2,0) and (3,0).

Since they are in the same coordinate, distance will be:

b = 3 - (-2)

b = 5

Area of the triangle is 10. So constant a is

$10=\frac{5.a}{2}$

5a = 10.2

a = 4

The constant a of the function y = a(x-3)(x+2) is 4.

7 0

2 years ago