Answer:
To solve the simultaneous equations
y=4x²+3 and y=8x−1, we need to find the values of x and y that satisfy both equations simultaneously.
We can do this by setting the expressions for y in both equations equal to each other:
4x²+3=8x−1
Now, we'll rearrange the equation to set it equal to zero:
4x²−8x+4=0
Next, we'll factor the quadratic equation:
4(x²−2x+1)=0
4(x−1)² =0
Now, we'll solve for x by setting each factor equal to zero:
x−1=0
x=1
Now that we have the value of x, we can substitute it into either of the original equations to find the corresponding value of y. Let's use the second equation:
y=8x−1
y=8(1)−1
y=8−1
y=7
So, the solution to the simultaneous equations is x=1 and y=7.
Now, let's plot the graphs of both equations to visualize the solution:
First Equation:
y=4x²+3
Second Equation:
y=8x−1
