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# Calculate points of intersection of the following two pairs of equations.

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Calculate points of intersection of the following two pairs of equations.

y=5x+6  and  y=9x-32

y=-0,5x+1,5  and  y=-4(x-3)

Feb 1, 2018

### Best Answer

#1
+18311
+2

We need the point(s) where   y = 5x+6    equals  y = 9x-32

or    5x+6 = 9x-32       solve for x     add 32 to each side of the equation

5x+38 = 9x           subtract 5x from both sides

38 = 4 x

9.5 = x           Now substitute theis 'x' into one of the equations to find 'y'

y= 5(9.5) +6        y= 53.5      so   x,y  =  9.5 , 53.5

(you can sub 'x' in to the other equation to see if you get the same result as a check)

0.5x+1.5= -4(x-3)

= -4x +12       add 4x to both sides

4.5x +1.5 =12                 Subtract 1.5 from both sides

4.5x = 10.5                      Divide by 4.5

x = 2 1/3

then sub  this 'x' in to one of the other equations to find 'y'

y=-4(x-3)=-4x+12

= -4 (2 1/3) + 12 = 2 2/3       x,y = 2 1/3 , 2 2/3

Feb 1, 2018
edited by ElectricPavlov  Feb 1, 2018

### 1+0 Answers

#1
+18311
+2
Best Answer

We need the point(s) where   y = 5x+6    equals  y = 9x-32

or    5x+6 = 9x-32       solve for x     add 32 to each side of the equation

5x+38 = 9x           subtract 5x from both sides

38 = 4 x

9.5 = x           Now substitute theis 'x' into one of the equations to find 'y'

y= 5(9.5) +6        y= 53.5      so   x,y  =  9.5 , 53.5

(you can sub 'x' in to the other equation to see if you get the same result as a check)

0.5x+1.5= -4(x-3)

= -4x +12       add 4x to both sides

4.5x +1.5 =12                 Subtract 1.5 from both sides

4.5x = 10.5                      Divide by 4.5

x = 2 1/3

then sub  this 'x' in to one of the other equations to find 'y'

y=-4(x-3)=-4x+12

= -4 (2 1/3) + 12 = 2 2/3       x,y = 2 1/3 , 2 2/3

ElectricPavlov Feb 1, 2018
edited by ElectricPavlov  Feb 1, 2018