Question

pair if possible or state No Solution or in er a mental or written check into both e ations by Substitution: (x,y) 3y+2x=-5 y=4x+17 y=1

Answer 1

The simultaneous equations are solved using substitution, resulting in the pair (x, y) = (-4, 1), which is confirmed by substituting the values back into the original equations.

Step-by-step explanation:

To solve the simultaneous equations provided in the question, we will use the substitution method. The student has been given two equations:

• 3y + 2x = -5
• y = 4x + 17

First, we note that the second equation gives us a value for y directly in terms of x. We can use this to substitute for y in the first equation.

Step 1: Substitute the second equation into the first equation:

3(4x + 17) + 2x = -5

Step 2: Solve the resulting equation for x:

12x + 51 + 2x = -5
14x = -56
x = -4

Step 3: Now that we have a value for x, substitute it back into the second equation to find y:

y = 4(-4) + 17
y = -16 + 17
y = 1

Therefore, the solution to the simultaneous equations is the pair (x, y) = (-4, 1).

To perform a mental or written check, we can substitute the values of x and y back into both original equations:

• 3(1) + 2(-4) = 3 - 8 = -5
• 1 = 4(-4) + 17 = -16 + 17 = 1

Both equations are satisfied, confirming the solution.