Question

Solve the simultaneous equations 2x+3y=13 4x-y=-2

Answer 1

In order to find the unknown variables x and y we need to simplify these equations in the way that will make it possible for us to get rid of either x or y variable, and make it easier to solve the remaining variable.

This method is known as Elimination, which is one of the methods how to solve a system of linear equations.

We need to rewrite the equations so that when the equations are added, one of the variables is eliminated. In simple terms, we need to get same number of x's or the same number of y's, but with an opposite sign, in both equations.

(1) 2x - 3y =13

(2) 3x + y = 3

You can multiply equation (2) by 3, then add equations (1) and (2) to form equation (3) with just one variable.

(2) 3*(3x+y) = 3*(3)

(2) 9x + 3y = 9

(1) 2x - 3y = 13

(3) 9x + 3y + 2x - 3y = 9 + 13

(3) 11x = 22

(3) x = 2

Then substitute our value for x back to one of the original equations and find what the value of y is.

2x - 3y = 13

2*(2) - 3y = 13

4 - 3y =13

- 3y = 9

y = - 3

Afterwards we can check our results by substituting our variables back into the original equations.

2*(2) - 3*(- 3) = 13

3*(2) + (- 3) = 3

Problem solved :)

Answer 2

2x + 3y = 13
4x - y = -2

In the second equation, subtract 4x from both sides.

-y = -2 - 4x

Divide both sides by -1.

y = 2 + 4x

Put this into the first equation in place of y.

2x + 3(2 + 4x) = 13

Multiply everything in the parenthesis by 3.

2x + 6 + 12x = 13

Combine like terms.

14x + 6 = 13

Subtract 6 from both sides.

14x = 7

Divide 14 on both sides.

x = 7 / 14

x = 0.5

Put this into the second equation in place of x.

4(0.5) - y = -2

2 - y = -2

Subtract 2 from both sides.

-y = -4

Divide both sides by -1.

y = 4

So x = 0.5 and y = 4.

Hope this helps!