What ordered pair is a solution to the system of equations.?

Question

-6x - 7y = 65
4x + 3y = -35

Answer 1

If you plot those two lines, the solution is the place where they cross each other (if they do)... but.. let's set them up in Slope-Intercept form: y = mx + b, where m is the slope and b is the y-intercept.

-6x - 7y = 65 ==> y = -(6x +65)/7 ==> y = -(6/7)x - 65/7

4x + 3y = -35 ==> y = (-4x -35)/3 ==> y = -(4/3)x - 35/3

since the slopes are different, the lines WILL cross and there is only 1 solution (if they had been the same slope then either there would have been no solution or infinite solutions)

one way to find the solution..

-6x -7y = 65 ==> multiply equation by 2 ==> -12x -14y = 130
4x + 3y = -35 ==> multiply equation by 3 ==> 12x + 9y = -105
now add the two equations to eliminate x ==> 0x -5y = 25
or... solving -5y = 25 for y... you get y = -5

now plug this value into one of the equations and solve for x:

4x + 3(-5) = -35 ==> 4x - 15 = -35 ==> 4x = -20 ==> x = -5

so your solution is (-5, -5)

Answer 2

These are both linear equations, so, there will be 1, none, or infinite solutions depending upon whether the 2 lines cross, run parallel, or coincide.

Since they were given in Standard Linear form, the best method to use is the elimination method. Pick one of the coefficients, either of the x or the y variable, and find the least common multiple. For these 2 equations, it is easier to work with the x coefficient. The LCM of -6 and 4 is 12.

So, multiply the top equation by what it takes to change the -6 into a -12, a 2. The top equation becomes -12x + 14y = 130. Multiply the bottom equation by whatever it takes to change the coefficient on x into a +12. In this case, 3. The bottom equation becomes 12x + 9y= -105.

Since it is ok to add the same thing to both sides of an equation to form a new equation, take and add the two equations together.

-12x - 14y = 130
+12x + 9y = -105
----------------------------
0x -5y = 25

or

y = -5.

Since this resulted in a unique value for y, there will be a unique value for x since they were both linear equations.

4x + 3(-5) = -35
4x -15 = -35
4x = -20
x = -5

and the answer is (-5,-5) just like everyone else has been saying

Answer 3

You asked this question before. I tested it out, but the solution has to be both (5, 5) and (5, -5) at the same time. IN this case, there is no solution.

Edit: Oh, never mind, I forgot the negative sign in -6x-7y = 65. The solution is (-5, -5).

Answer 4

-6x-7y=65-----(1)
4x+3y=-35------(2)
(1)*2-----> -12x-14y=130
(2)*3-----> 12x+9y=-105
------------------------------------
adding, -5y=25
y=25/-5=-5
substituting in eqn(2), we get
4x-15=-35
4x=-35+15=-20
x=-20/4
x=-5
(-5,-5) is the pair satisfying the set of lin equations.
Note: Multiply the equations so that the coefficient of any one variable become equal irrespective of the sign. Keep the coefficient as small as possible to avoid dealing with large numbers in the equations. The LCM of the coefficients may be calculated. The LCM of 4 and 6 is 12. Simply using cross multiplication, keeps dealind with large numbers. The case is true with the next correspondent (Sherman81).

Answer 5

-6x - 7y = 65
4x + 3y = -35

Multiply top by 4 and bottom by 6

-24x - 28y = 260
24x + 18y = -210

-10y = 50
y = -5

-6x - 7y = 65
-6x - 7(-5) = 65
-6x + 35 = 65
-6x = 30
x = -5

(-5,-5)

Answer 6

Use 2x + a million for y interior the 1st equation. x + (2x+a million)=4 3x+a million=4 3x=3 x=a million Now which you realize the fee of x, basically positioned it on your y equation. that provide you with 2(a million)+ a million, so y equals 3. consequently, the ordered pair is (a million,3)

Answer 7

4(-6x-7y)=260
6(4x+3y)=-210
adding both the eqns
-10y=50
y=-5
-6x+35=65
-6x=30
x=-5
(-5,-5) is the sol

Answer 8

I believe (-5,-5)

Answer 9

It's obvious that it's (-5,-5).

Answer 10

(-5,-5)