# math

posted by .

the system of linear equations below has a unique solution for all but one value of a:

6 x−12 y=−6
58 x+a y=−58

What is this exceptional value for a?

• math -

unique solution means the lines intersected at only one point (intersecting lines),, thus lines that do not intersect don not have a solution (parallel lines)
if two lines are parallel, then their slopes must be equal,, thus get their slopes by writing them into the form:
y = mx + b
where m = slope, and b = y-intercept
*for 6x − 12y = −6,
6x − 12y = −6
-12y = -6 - 6x
y = (1/2)x + (1/2)
thus m = 1/2
*for 58x+ ay = −58,
58x+ ay = −58
ay = -58 - 58x
y = (-58/a)x - 58/a
thus m = -58/a

equating and solving for a:
1/2 = -58/a
a = -116

so there,, :)

• math -

## Similar Questions

1. ### Calc.

I am so confused with this last part of the unit! What in the world is going on: Use normal vectors to determine the interaction, if any, for each of the following pairs of planes. Give a geometric interpretation in each case and the …
2. ### Finite Math

Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions involving one parameter, enter the solution using t for the last variable. …
3. ### Math

Find a system of linear equations corresponding to the following augmented matrices: (a) 2 0 |0 3 −4 |0 0 1 |1 (b) 3 0 −2 |5 7 1 4 |−3 0 −2 1 |7 (c) 7 2 1 −3 |5 1 2 4 0 |1 (d) 1 0 0 0 |7 0 1 0 0 |−2 …
4. ### biology

Given the part of the molecule shown below, can the underlined atom participate in a hydrogen bond with an approriate bonding partner?

Evaluate each of the following. Show all your calculations. a) f'(3) if f(x)  = x^4 − 3x b) f' (−2) if f(x) = 2x^3 + 4x^2 − 5x + 8 c) f" (1) if f(X)  = −3x^2 − 5x + 7 …
6. ### MATH

For what integer 0<n<1000, does the following system of n linear equations have no complex solution?
7. ### math

the system of linear equations below has a unique solution for all but one value of a : 5 x - 5 y = 25 48 x + a y = 240 What is this exceptional value for a ?
8. ### math help pls pls

Two systems of equations are shown below: System A 6x + y = 2 −x − y = −3 System B 2x − 3y = −10 −x − y = −3 Which of the following statements is correct about the two systems of equations?
9. ### algebra

Solve the system of linear equations    x − 2y + 3z = 7 4x + 5y + z = −1 −x + y − 2z = −4 What is the value of z, y, and x?
10. ### Maths

Solve the following system of linear equations by addition. Indicate whether the given system of linear equations is consistent, inconsistent, or dependent. If the system is consistent, find the solution. {−7x + 7y −9x …

More Similar Questions