Question

Solve the system by substitution:
y = -3x + 10
y=-3x + 4
Please show the steps!

Answer 1

x=1, y=7

Explanation:

y = -3x + 10 - first equation

y=-3x + 4 - second equation

rearrange the expression to

-3x-y= -10

3x-y= -4

pick an equation and simplify; lets pick the second equation

3x-y= -4

`(3x)/(3) = (-4+y)/(3)`

divide 3 by both sides

x=
`(-4+y)/(3)` - third equation

substitute the value of x into an equation; lets pick the first equation

-3x-y= -10

-3
`((-4+y)/(3))`- y = -10

simplify. -3 cancels 3 so we are left with

-1(-4+y)-y = -10

simplify

4-y-y= -10

4-2y= -10

subtract 4 from both sides

-2y= -10-4

-2y= -14

divide -2 by both sides

y=7

substitute the value of y, (y=7) in an equation, we are using the second equation

3x-y= -4

3x-7= -4

3x = -4+7

3x= 3

divide 3 by both sides

x=1

so the answer is x=1, y=7