Question

Solve the equations x+y=17
xy-5x=32

Answer 1

To solve these equations, we can use substitution or elimination method.

Let's solve using substitution method:

From the first equation x + y = 17, we can rewrite it as y = 17 - x.

Substitute this value of y into the second equation:

(x)(17 - x) - 5x = 32

Simplify the equation:

17x - x^2 - 5x = 32

Combine like terms:

- x^2 + 12x - 32 = 0

Rearrange the equation:

x^2 - 12x + 32 = 0

Now, we have a quadratic equation. We can solve it by factoring:

(x - 4)(x - 8) = 0

Setting each factor equal to zero:

x - 4 = 0 or x - 8 = 0

Solving for x:

x = 4 or x = 8

Substitute these values of x back into the first equation x + y = 17 to find the corresponding values of y:

For x = 4:

4 + y = 17
y = 17 - 4
y = 13

So, one solution is x = 4 and y = 13.

For x = 8:

8 + y = 17
y = 17 - 8
y = 9

So, the other solution is x = 8 and y = 9.

Therefore, the solutions to the given equations are x = 4, y = 13 and x = 8, y = 9.