If you were solving a system of equations and you came to a statement like 1 = 3, what do you know about the solution(s) to this system?
Solve the following system and show all of your work.
x − 2y = 14
x + 3y = 9
Stacey Warren - Expert brainly.com
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it tells you that there is no solution
i.e. if graphing the 2 equations, the lines do NOT cross.
x- 2y = 14
x+3y = 9
need a common factor to cancel x to to solve for y though the cancelling of terms . -1 is good. So I'll use it
x-2y = 14
(-1) x +3y = 9(-1) - Multiplying a negative number to one of the equation to both sides of it to change a variable from a negative value to a positive one or vise verse to cancel one of the terms to solve for the other though the addition of terms
x -2y = 14
---------------- - Multiplication and addition of terms
0x -5y = 5
-5y = 5 - Addition
1/-5* -5y = 5 * 1/-5 - Multiplying the reciprocal of a coefficient to both sides of the equation to solve for y
y = 5/-5 - Multiplication
y = -1 - Division
let solve for x
x-2y = 14 - one of the original equations
x - 2(-1) = 14 - substituting y with -1
x + 2 = 14 - Multiplication
x + 2 -2 = 14- 2 - Adding the additive inverse of a number to both sides of the equation to move it to the other side of it
x= 12 - Addition
x- 2y = 14
x+3y = 9 - original equation
12-2(-1) = 14
12+ 3(-1) = 9 - substituting y and x with -1, and 12
12+ 2 = 14
12-3 = 9 - Multiplication
14 = 14
9 = 9 - Addition ...