Solve the system of equations algebraically. Show all your steps.
y=x^2+2x
y=3x+20
Can someone pease help me? I don't think I'm right.
Would it be x=-4, y=8
Then, x=5,y=35??
To solve the system of equations algebraically, we need to find the values of x and y that satisfy both equations simultaneously.
Step 1: Set the two equations equal to each other:
x^2 + 2x = 3x + 20
Step 2: Move all terms to one side to obtain a quadratic equation:
x^2 + 2x - 3x - 20 = 0
Step 3: Combine like terms:
x^2 - x - 20 = 0
Step 4: Factor the quadratic equation:
(x - 5)(x + 4) = 0
So, either x - 5 = 0 or x + 4 = 0
Step 5: Solve for x:
For x - 5 = 0, we have x = 5
For x + 4 = 0, we have x = -4
So, the possible solutions for x are x = 5 and x = -4.
Step 6: Substitute the values of x into one of the equations to find the corresponding values of y:
For x = 5, substitute it into y = x^2 + 2x:
y = (5)^2 + 2(5) = 25 + 10 = 35
For x = -4, substitute it into y = x^2 + 2x:
y = (-4)^2 + 2(-4) = 16 - 8 = 8
Hence, the solution to the system of equations is x = 5, y = 35 and x = -4, y = 8.
To solve the system of equations algebraically, we can set the two equations equal to each other because they both equal to y:
x^2 + 2x = 3x + 20
Now, we can simplify the equation by moving all terms to one side:
x^2 + 2x - 3x - 20 = 0
Simplifying further:
x^2 - x - 20 = 0
Now, we need to factorize this quadratic equation. We look for factors of -20 that add up to -1. The factors are -5 and 4:
(x - 5)(x + 4) = 0
Setting each factor equal to zero and solving for x:
x - 5 = 0 or x + 4 = 0
x = 5 or x = -4
Now that we have the values of x, we can substitute them back into either of the original equations to find the respective values of y.
Substituting x = 5 into the first equation:
y = (5)^2 + 2(5)
y = 25 + 10
y = 35
So one solution is x = 5, y = 35.
Substituting x = -4 into the first equation:
y = (-4)^2 + 2(-4)
y = 16 - 8
y = 8
So the other solution is x = -4, y = 8.
Therefore, the system of equations has two solutions:
x = 5, y = 35
and
x = -4, y = 8
can you not check your answers?
(-4,8) works
(5,35) works