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We can find out whether lines are perpendicular by comparing their gradients. Each gradient should be the negative reciprocal of the other - for example, 3/2 and -2/3, or 4 and -1/4. (Writing the number a...

The first thing you should always do when approaching questions like this is to get the numbers on one side and the letters on the other. This makes the equation simpler and helps you to solve it. By addi...

z = 3x + 5y 41 = 3(7) +5y 41= 21 + 5y 20 = 5y 4 = y y = 4 2y = 8

When we have a quadratic (ax² + bx + c = 0) we can "complete the square" to solve for x. For example x² + 8x + 7 = 0. First look at the x² + 8x, in particular th...

Firstly, since only one equation is linear, substitution must be used. This will allow us to make a quadratic equation with one variable and solve for X and Y. To do this, I will make Y the subject of the...