Solve the simultaneous equations: 2x​+3y​=4, 4x​−6y​=0.

Solve for a and b: 3a​−5b​=−2, 6a​+2b​=7.

Solve the quadratic equation by factoring: 2x2−5x−3=0.

Solve by factoring: x(x+7)=18.

Solve the quadratic equation by completing the square: x2−6x+4=0.

Solve by completing the square: 2x2+8x−5=0.

Write down the quadratic formula for solving ax2+bx+c=0.

Solve the quadratic equation using the formula: 3x2+5x−1=0. (Give your answer to two decimal places).

Solve: x−14​−x3​=1.

The product of two consecutive positive odd integers is 143. Find the integers.

The length of a rectangle is 5 cm more than its width. If its area is 84 cm², find its dimensions.

The hypotenuse of a right-angled triangle is 17 cm. The sum of the lengths of the other two sides is 23 cm. Find the lengths of the other two sides.

The sum of a number and its reciprocal is 1225​. Find the number.

Solve: 3x​+y=3, x−2y​=4.

A two-digit number is such that the product of its digits is 18. If 27 is subtracted from the number, the digits interchange their places. Find the number.