solve the system of equations algebraically. show all your steps. y=x^2+2x y=3x+20
Can someone show me step by step on how to get the answer it's, there are answers like this that is going to be on my math test and I don'tget it.
By the way, this math not science.
Sorry for my spelling, rushed it.
Since both = y, they must be equal to each other.
x^2+2x = 3x+20
Solve for x, then y.
To solve the system of equations algebraically, we can set the two equations equal to each other and solve for the value(s) of x. Let's go through the steps:
Step 1: Write the equations:
Equation 1: y = x^2 + 2x
Equation 2: y = 3x + 20
Step 2: Set the equations equal to each other:
x^2 + 2x = 3x + 20
Step 3: Rearrange the equation:
x^2 + 2x - 3x - 20 = 0
Step 4: Combine like terms:
x^2 - x - 20 = 0
Step 5: Factor the equation:
(x - 5)(x + 4) = 0
Step 6: Set each factor equal to zero and solve for x:
x - 5 = 0 --> x = 5
x + 4 = 0 --> x = -4
So, the values of x that satisfy the system of equations are x = 5 and x = -4.
Step 7: Substitute the values of x back into one of the original equations to find the corresponding y-values:
- For x = 5:
Substituting x = 5 into Equation 1: y = (5)^2 + 2(5) = 25 + 10 = 35
So, when x = 5, y = 35.
- For x = -4:
Substituting x = -4 into Equation 1: y = (-4)^2 + 2(-4) = 16 - 8 = 8
So, when x = -4, y = 8.
Therefore, the solution to the system of equations is (x, y) = (5, 35) and (-4, 8).