At least one of the equations in each set is not a linear equation.

Substitution is the replacement of a variable or expression by its equivalent.

2x - y = 4

2x = 4 + y (add y)

x^2 + (

x^2 + 4x^2 - 16x + 16 = 13 (carry out the square operation)

5x^2 - 16x + 3 = 0 (subtract 13)

(5x - 1)(x - 3) = 0 (factor)

x = 1/5, 3 (find solutions to make the factors zero)

y = -3 3/5, 2 (find corresponding values for y)

4x^2 + 9(4x^2 - 16x + 16) = 72

40x^2 -144x + 72 = 0 (rewrite to standard form)

5x^2 - 18x + 9 = 0 (divide by 8)

(5x-3)(x-3) = 0 (factor)

x = (3/5, 3); y = -2 4/5, 2

4x^2 + 9(

4x^2 + 9x - 63 = 0 (put in standard form)

(4x+21)(x-3) = 0 (factor it)

x = -21/4, 3 (only the positive solution is useful here)

3+1 = y^2, so y = +/- 2

Substitution is the replacement of a variable or expression by its equivalent.

**1)**Solve the second equation for y, then substitute for y in the first equation.2x - y = 4

2x = 4 + y (add y)

**2x - 4**= y (now we have an equivalent for y that we can use in the first equation)x^2 + (

**2x - 4**)^2 = 13 (make the substitution)x^2 + 4x^2 - 16x + 16 = 13 (carry out the square operation)

5x^2 - 16x + 3 = 0 (subtract 13)

(5x - 1)(x - 3) = 0 (factor)

x = 1/5, 3 (find solutions to make the factors zero)

y = -3 3/5, 2 (find corresponding values for y)

**The solutions are (x, y) = (1/5, -3 3/5) and (3, 2)**.**2)**Use the same substitution as before.4x^2 + 9(4x^2 - 16x + 16) = 72

40x^2 -144x + 72 = 0 (rewrite to standard form)

5x^2 - 18x + 9 = 0 (divide by 8)

(5x-3)(x-3) = 0 (factor)

x = (3/5, 3); y = -2 4/5, 2

**The solutions are (x, y) = (3/5, -2 4/5), (3, 2)**.**3)**You can solve the second equation for y^2 and make a substitution for that**.**x - y^2 = -1**x+1**= y^24x^2 + 9(

**x+1**) = 72 (make the substitution for y^2)4x^2 + 9x - 63 = 0 (put in standard form)

(4x+21)(x-3) = 0 (factor it)

x = -21/4, 3 (only the positive solution is useful here)

3+1 = y^2, so y = +/- 2

**The solutions are (x, y) = (3, 2), (3, -2)**.