Find the equation of the line that passes through (–3, 2) and the intersection of the lines x–2y=0 and 3x+y+5=0. I need the intersection point of the lines and the equation of the line.

x+y+5=0

Step-by-step explanation:

the intersection of x-2y=0 and 3x+y+5 is (;)

=> the line : x+y+5=0

Step-by-step explanation:

Find intersection of the given lines :

x - 2y = 0 => x = 2y ----------- ( 1 )

3x + y = - 5 -------------------- ( 2 )

Substitute ( 1 ) in ( 2 ) :

                               3x + y = - 5

                               3 ( 2y ) + y = - 5

                                6y + y = - 5

                                  7y = - 5

Substitute y in ( 1 ) :

                            x = 2y

To find the equation of the line passing through ( - 3, 2) and point of intersection :

Standard equation of a line : y = mx + b , where m is the slope, b is the y intercept.

So step 1 : Find slope , m:

Step 2 : Equation of the line :

i dont know men

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.