2x-y²=1 3x+y=4 Heelp...
1 answer:
So first we solve for y in second equation
3x+y=4
y=4-3x
sub for y in first equiton
2x-(4-3x)^2=1
2x-(16-12x-12x+9x^2)=1
2x-(16-24x+9x^2)=1
2x-16+24x-9x^2=1
-9x^2+26x-16=1
times -1 both sides
9x^2-26x+16=-1
add 1 to both sides
9x^2-26x+17=0
factor
(x-1)(9x-17)=0
set each to zero
x-1=0
x=1
9x-17=0
9x=17
x=17/9
so sub back to find y
y=4-3x
y=4-3(1)
y=4-3
y=1
(1,1)
y=4-3x
y=4-3(17/9)
y=4-17/3
y=12/3-17/3
y=-5/3
(17/9,-5/3)
the 2 intersection points are
(1,1) and
3x+y=4
y=4-3x
sub for y in first equiton
2x-(4-3x)^2=1
2x-(16-12x-12x+9x^2)=1
2x-(16-24x+9x^2)=1
2x-16+24x-9x^2=1
-9x^2+26x-16=1
times -1 both sides
9x^2-26x+16=-1
add 1 to both sides
9x^2-26x+17=0
factor
(x-1)(9x-17)=0
set each to zero
x-1=0
x=1
9x-17=0
9x=17
x=17/9
so sub back to find y
y=4-3x
y=4-3(1)
y=4-3
y=1
(1,1)
y=4-3x
y=4-3(17/9)
y=4-17/3
y=12/3-17/3
y=-5/3
(17/9,-5/3)
the 2 intersection points are
(1,1) and
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The given equation is,
Thus, option (C) is the correct solution.
The solution of the equation is
Step-by-step explanation:
To simplify an equation of x
- Simplify each side of the equation
- Collect x in side and the numerical terms in the other side
- Find the value of x
∵ The equation is
- Multiply all terms of the equation by 4 to cancel the denominator
of the 2nd term in the left hand side
∵ The equation is
∴ 8x + (1 - x) = 12
∴ 8x + 1 - x = 12
- Add like terms
∴ (8x - x) + 1 = 12
∴ 7x + 1 = 12
- Subtract 1 from both sides
∴ 7x = 11
- Divide both sides by 7
∴
The solution of the equation is
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