math/algebra

posted by Diana

solve each of the following systems by substitution.
16) 5x -2y = -5
y - 5x = 3
20) 8x -4y = 16
y = 2x - 4
28) 4x -12y = 5
-x + 3y = -1

Step one: Solve on of the equations for one of the variables.
y=2x-4
Step two:Substitute the expression for the variable found in step one into the other equation.
8x-4(2x-4)=16
Step three:Solve the equation from step two to find the value of one variable.
Use the distributive property
8x-4(2x-4)=16
8x-8x+16=16
x+16=16
-16 -16
x=0
Step four:Substitute the value found in step three in any equation containing both variables to find the value of the other variable.
y=2x-4
y=2(0)-4
y=0-4
y=-4
step five: check the proposed solution in the orginal system.
8(0)-4(-4)=16
0+16=16
16=16
The equation is equal, so it is correct.
#28
4x-12y=5 -x+3y=-1
+x +x
3y=-x or -3y=x

4(-3y)-12y=5 4x-12(5)=5
-12y-12y=5 4x-60=5
y=5 +60 +60
4x=65
x=65/4

4(65/4)-12(5)=5
260/4 - 60=5
65 - 60 = 5
5 = 5
it's correct

I hope I helped

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