solve and check x + y = -2; y = 4x - 7

Question

solve for y and x intercepts.

Answer 1

Substitution Method :

The system of equations are x + y = - 2 and y = 4x - 7.

Step 1 : The equation 2 : y = 4x - 7 is already solved for y.

Step 2 : Substitute 4x - 7 for y in the equation 1 : x + y = - 2 to find the value of x.

x + (4x - 7) = - 2

5x - 7 = - 2

Add 7 to each side.

5x - 7 + 7 = - 2 + 7

5x = 5

Divide each side by 5.

5x/5 = 5/5

x = 1.

 

Step 3 : Substitute 1 for x in either equation to find y.

Equation 2 : y = 4x - 7

y = 4(1) - 7

y = - 3.

The solution (x, y) = (1, - 3).

 

CHECK :

To check the solution, substitute (x, y) = (1, - 3) in each original equation.

Equation 1 : x + y = - 2     |   Equation 2 : y = 4x - 7

          (1) + (- 3) ≟ - 2    |                 (- 3) ≟ 4(1) - 7

                       - 2 = - 2    |                     - 3 = - 3