# SAT prep algebra question: System of equations: 5x-3y=10 and 6y=kx-42

#### Illvoices

##### Junior Member
{5x-3y=10
{6y=kx-42}

These two equations belong to the same set. I just couldn't find the proper way to place the colon in a big chunk.

In the system of linear equations above, k represents a constant.If the system of the equation has no solution, what is the value of 2k?

*Can someone tell me how to solve this question I don't think the kaplan booklet really tells you how.

#### j-astron

##### Junior Member
Well, first of all, rearrange things to express them in the same form

5x - 3y = 10

kx - 6y = 42

Do you know how to solve a system of equations in general? Try using each equation to eliminate one of the variables, by expressing it in terms of all the others. For example, if you solved the first equation for 'x', you could then substitute that expression for 'x' into the second equation, and everything would now be in terms of only one variable: y. You would be able to solve the second equation for y, but presumably there would be some value of k for which you wouldn't be able to obtain a solution to the second equation.

#### Illvoices

##### Junior Member
Well, first of all, rearrange things to express them in the same form

5x - 3y = 10

kx - 6y = 42

Do you know how to solve a system of equations in general? Try using each equation to eliminate one of the variables, by expressing it in terms of all the others. For example, if you solved the first equation for 'x', you could then substitute that expression for 'x' into the second equation, and everything would now be in terms of only one variable: y. You would be able to solve the second equation for y, but presumably there would be some value of k for which you wouldn't be able to obtain a solution to the second equation.
Ok I think i'll be using khan academy until i know what the kaplan booklet is telling me. thanks for the lesson =)

#### stapel

##### Super Moderator
Staff member
{5x-3y=10
{6y=kx-42}

These two equations belong to the same set. I just couldn't find the proper way to place the colon in a big chunk.

In the system of linear equations above, k represents a constant.If the system of the equation has no solution, what is the value of 2k?

*Can someone tell me how to solve this question I don't think the kaplan booklet really tells you how.
A system of equations has a solution where the graph of the corresponding lines cross. If the system has no solution, then the lines must not cross. What sort of lines must they then be? What does this tell you about the values of the slopes of the two lines? So what value must "k" be? 