Question

Solve the simultaneous equations y=x-2 and y=3x+5

Answer 1

The simultaneous equations y = x - 2 and y = 3x + 5 are solved by equating the two expressions for y and finding that x = -3.5 and y = -5.5.

Step-by-step explanation:

To solve the simultaneous equations y=x-2 and y=3x+5, we need to find a common solution for x and y that satisfies both equations simultaneously.

First, we can equate the two expressions for y since they are equal to the same variable: x - 2 = 3x + 5.

Next, we solve for x by rearranging the terms: x - 3x = 5 + 2 which simplifies to -2x = 7. Then we divide both sides by -2 to find x: x = -7/2 or x = -3.5.

Now, we can substitute x back into one of the original equations to find y. Using y = x - 2: y = -3.5 - 2, which gives us y = -5.5.

The solution to the simultaneous equations is x = -3.5 and y = -5.5. We have determined the values for both unknowns using algebraic steps and substitution.

Answer 2

(- 3.5, - 5.5 )

Step-by-step explanation:

Given the 2 equations

y = x - 2 → (1)

y = 3x + 5 → (2)

Substitute y = 3x + 5 into (1)

3x + 5 = x - 2 ( subtract x from both sides )

2x + 5 = - 2 ( subtract 5 from both sides )

2x = - 7 ( divide both sides by 2 )

x = - 3.5

Substitute x = - 3.5 into either of the 2 equations and evaluate for y

Substituting into (1)

y = - 3.5 - 2 = - 5.5

Solution is (- 3.5, - 5.5 )