Solve the system: y = x2 – 5, y = 2x - 2

To solve the system of equations y = x^2 - 5 and y = 2x - 2, we can use the method of substitution or elimination. Here, since both equations are already solved for y, we can set them equal to each other and solve for x.

Step 1: Set the two equations equal to each other:

x^2 - 5 = 2x - 2

Step 2: Rearrange the equation to one side to set it equal to zero (this is necessary for factoring or using the quadratic formula):

x^2 - 2x - 3 = 0

Step 3: Factor the quadratic equation:

(x - 3)(x + 1) = 0

Step 4: Set each factor equal to zero and solve for x:

x - 3 = 0 => x = 3

x + 1 = 0 => x = -1

So the solutions for x are x = 3 and x = -1.

Step 5: Substitute x into one of the original equations to solve for y. We can use the first equation y = x^2 - 5:

For x = 3: y = (3)^2 - 5 = 9 - 5 = 4

For x = -1: y = (-1)^2 - 5 = 1 - 5 = -4

So the solutions to the system of equations are (3, 4) and (-1, -4).

To solve the system of equations y = x^2 - 5 and y = 2x - 2, we can use the method of substitution or elimination. Here, since both equations are already solved for y, we can set them equal to each other and solve for x.

Step 1: Set the two equations equal to each other:

x^2 - 5 = 2x - 2

Step 2: Rearrange the equation to one side to set it equal to zero (this is because we're going to use the quadratic formula to solve for x):

x^2 - 2x - 3 = 0

Step 3: Factor the quadratic equation:

(x - 3)(x + 1) = 0

Step 4: Set each factor equal to zero and solve for x:

x - 3 = 0 => x = 3

x + 1 = 0 => x = -1

So, the solutions for x are x = 3 and x = -1.

Step 5: Substitute x into one of the original equations to solve for y. We'll use the simpler one, y = 2x - 2:

For x = 3, y = 23 - 2 = 4 For x = -1, y = 2(-1) - 2 = -4

So, the solutions to the system of equations are (3, 4) and (-1, -4).

To solve the system of equations y = x^2 - 5 and y = 2x - 2, we can use the method of substitution or elimination. Here, since both equations are already solved for y, we can set them equal to each other and solve for x.

Step 1: Set the two equations equal to each other:

x^2 - 5 = 2x - 2

Step 2: Rearrange the equation to one side to set it equal to zero:

x^2 - 2x - 3 = 0

Step 3: Factor the quadratic equation:

(x - 3)(x + 1) = 0

Step 4: Set each factor equal to zero and solve for x:

x - 3 = 0 => x = 3

x + 1 = 0 => x = -1

So, the solutions for x are x = 3 and x = -1.

Step 5: Substitute x into one of the original equations to solve for y:

For x = 3, y = (3)^2 - 5 = 9 - 5 = 4

For x = -1, y = (-1)^2 - 5 = 1 - 5 = -4

So, the solutions to the system of equations are (3, 4) and (-1, -4).