2x + 6y = 93x - 12y = 15Chose the second equation because you can simplify it.3x - 12y = 15 divide by 3 to both sidesx - 4y = 5 add 4y to both sidesx = 4y + 5Replace 4y + 5 for x to the first equation.2x + 6y = 92(4y + 5) + 6y = 98y + 10 + 6y = 914y = -1y = -1/14x = 4y + 5x = 4(-1/14) + 5x = -2/7 + 5x = -2/7 + 35/7x = 33/7
There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.
This can happen in different ways: a) More variables than equations. For instance, a single equation with two variables (such as x + y = 15), two equations with three variables, two equations with four variables, etc. b) To of the equations describe the same line, plane, or hyper-plane - this, in turn, will result in that you "really" have less equations than it seems. For example: y = 2x + 3 2y = 4x + 6 The second equation is simply the first equation multiplied by 2.
You can't answer this question without setting that expression equal to something. Right now, your equation reads 4x+15=?, essentially created a system of two variables with only one equation, which is unsolvable.
The first step is to solve one of the equations for one of the variables. This is then substituted into the other equation or equations.
You use substitution when you can solve for one variable in terms of the others. By substituting, you remove one variable from the equation, which can then be solved. Once you solve for one variable, you can use substitution to find the other.
If you mean x+2y = -2 and 3x+4y = 6 then by solving the simultaneous equations by substitution x = 10 and y = -6
By elimination and substitution
The first step is usually to solve one of the equations for one of the variables.Once you have done this, you can replace the right side of this equation for the variable, in one of the other equations.
The first step is to show the equations which have not been shown.
Isolating a variable in one of the equations.
You'd need another equation to sub in
I'll assume the simplified case of two equations, with two variables each. Some of the methods can be extended to more complicated cases.Substitution: Solve for one variable in one equation, replace it in the other equation.Setting two quantities equal: For example, if 5x + 3y = 10, and 5x - 2y = 0, solve each equation for "5x", and set the two equal, with the result: 10 - 3y = 2y.Addition/subtraction: Add or subtract one equation (or a multiple of one equation) to the other. In the previous example, if you subtract the second equation from the first, you get an equation that doesn't contain x.In any of these cases, after solving for a single variable, replace in one of the original equations to get the other variable.
Substitution method: from first equation y = 5x - 8. In the second equation this gives 25x - 5(5x - 8) = 32 ie 25x - 25x + 40 = 32 ie 40 = 32 which is not possible, so the system has no solution. Multiplication method: first equation times 5 gives 25x - 5y = 40, but second equation gives 32 as the value of the identical expression. No solution.
how do you use the substitution method for this problem 2x-3y=-2 4x+y=24
You are trying to find a set of values such that, if those values are substituted for the variables, every equation in the system is true.