Can someone please help solve these simultaneous equations?

If you have a graphing calculator, an easy way to solve these is to graph them and see where the lines intersect. (see graphic) Cramer's rule gives straightforward solution that will give you a solution just by plugging numbers into a formula. You must add 7 to your first equation to get it in the form 3X + Y = 13 before you apply Cramer's rule.

(see source link) The Elimination method lets you reduce the two equations to one equation in one variable. To use that, you multiply one or both equations by numbers so that the result is a pair of equations with one of the variables having opposite signs. Then you add those equations to eliminate that variable.

For example, you can multiply your first equation by -2 so the Y term has coefficient -2, opposite that in the second equation. Or, you can multiply the second equation by -3 so the X term has opposite sign to the X term in the first equation. (Or you can do both.) Of course, you always do the same thing to both sides of the equation.

.. -2(3X + Y - 7) + (X + 2Y) = -2(6) + (1) ... -2 times the first added to the second .. -5X + 14 = -11 ... simplify. Notice Y terms are gone .. X = (-11 - 14)/(-5) = 5 ... subtract 14 and divide by -5 to find X .. -3(X + 2Y) + (3X + Y - 7) = -3(1) + 6 ... -3 times the second added to the first .. -5Y - 7 = 3 ... simplify. Notice X terms are gone .. Y = (3 + 7)/(-5) = -2 ... add 7 and divide by -5 to find Y.

Now we have (X, Y) = (5, -2). The Substitution method has you solve one equation for one of the variables and use that expression in the other equation. Either equation can be used for the first step.

It is often easier if you pick one that simplifies the coefficients involved. .. X = 1 - 2Y ... solve the second equation for X by subtracting 2Y .. 3(1 - 2Y) + Y - 7 = 6 ... substitute the above expression for X in the first equation .. -5Y - 4 = 6 ... simplify .. Y = (6 + 4)/(-5) = -2 ... add 4 and divide by -5 to find Y. .. X = 1 - 2(-2) = 5 ... substitute the value for Y into the equation for X.

Now we have (X, Y) = (5, -2). There are also any number of on-line equation solvers you can use. One of them is at the second source link.

It requires you to do a bit of rearranging on your first equation to get it into standard form (as for Cramer's method).

There are 4 methods. I will use elimination method 3x + y - 7 = 6? 6x + 2y = 26 x + 2y = 1?

-1x + -2y = -1 Add sides and simplify: 5x + 0y = 25 Since the coefficient of y is 0, then for all practical purposes y has been eliminated, ergo the name of the method. Solve for x, then take that value to one of the original equations and solve for y. Use the other equation to check your results.

GL!

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