Saturday

December 20, 2014

December 20, 2014

Posted by **Rebecca** on Saturday, March 5, 2011 at 1:55pm.

a) No solution b) Infinitely many solutions c) One solution

I know how to figure out if two linear systems have a solution, but I don't understand how you could figure out if just one linear system has a solution. Help please?

- Grade 10 Math -
**jai**, Saturday, March 5, 2011 at 6:42pm(a) no solution

- Grade 10 Math -
**jai**, Saturday, March 5, 2011 at 6:54pm(a) no solution

recall that two linear equations have no solution if they are parallel (solution means they meet at a certain point),, thus the two equations, in order to be parallel must have the SAME SLOPE.

to determine the slope of the given equation, we rewrite it in this form:

y = mx + b

where m = slope and b = y-intercept,, so x + y = 4 becomes:

y = -x + 4

where m = -1

now that we know the slope, we can now formulate a new equation with slope=1,, thus we only change the value of b in order to have a parallel equation,, an example would be:

y = -x + 1

(b) infinitely many solutions

here, it means that the two linear equations coincide meaning they have the SAME SLOPE and Y-INTERCEPT,, this means that the equations are equal, and most of the time, they are just the multiple of each other.

for the given equation, we can just multiply any number to both sides of the equation to formulate the coinciding equation,, for instance we multiply it by 2:

2(x + y = 4)

2x + 2y = 8

(c) one solution

it means that the two equation meet at EXACTLY ONE POINT,, thus the other equation must have at least, a DIFFERENT SLOPE,, an example would be:

x + 2y = 4

where they meet at point (4,0)

hope this helps~ :)

- Grade 10 Math -
**jai**, Saturday, March 5, 2011 at 6:55pmsorry for the first post by the way~ ^^;

i just accidentally hit the enter button~ ^^;

**Answer this Question**

**Related Questions**

math - two systems of equations are giving below for each system choosethe best ...

MAT222 - -x+2y=-2 x-2y=2 the system has no solution the system has a unique ...

Algebra - Suppose a linear system of equations has 2012 equations and 2013 ...

Algebra 2 Helpp :( - QUESTIONS (vvv) (1) Solve the system by subsitution 2x + y...

MAT222 - -x+4y=4 x-4y=-4 the system has no solution the system has a unique ...

algebra 2 - Classify the system , and determine the number of solutions. This ...

math - two systems of equations are given below for each system, choose the best...

Math 116 - Identify the solution (s) of the system of equations, if any. x=1 y=1...

Math - Determine if f could be a linear function x 0 1 2 3 4 f(x) 3 5 7 11 15 is...

Intermediate Algebra - Solve the system of equations by graphing. Then classify ...