The equals sign ( = ). In fact it defines any equation, linear or not, since an equation is a statement that a particular value or term is equal to, so the result of solving, a second set of terms and operators. Any other symbols would be particular to the equation you have derived or are trying to solve.
Algebraic equations with two variables will need two equations to be able to solve it. Then, you can solve it with either substitution, adding/subtracting them together, or graphing! Those are the basic steps... For example: An instance of substitution: 2x + 1 = y + 2 x + y = 3 You could isolate y in the second equation to equal y = 3-x. Then in the first equation, substitute y with what it equals to 2x + 1 = 3-x+2 Then you can solve for x!
From first equation, -y = 3x + 3. Substitute in second equation: -3x + 5(3x + 3) = -21 ie 12x = -36 so x = -3 and y = -(-9 + 3) = 6. Easier method: subtract first equation from second giving -4y = -24 so y = 6, this in first equation gives -6 = 3x + 3, ie 3x = -9 so x = -3
When you are solving a 2-step equation, you do the opposite of a 1-step equation. You do addition and subtraction first, then the multiplication second. Example: 2x + 9=16 -9 -9 2x=7 Now it's a 1-step equation 2x=7 /2 /2 Your answer would be 3.5 To check all you do is replace the variable with your answer. 2x + 9=16 2(3.5) + 9=16
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If it's a simultaneous equation in x and y variables then x or y may be solved before substitution.
True
A nonlinear equation does not produce a straight line and the exponent is to the second power or more. x square plus 3y =5 is an example of a nonlinear equation.
Nonlinear
Since the second equation is already solved for "y", you can replace "y" by "9" in the other equation. Then solve the new equation for "x".
If r = 5z, then 15z = 3y, then r = y. This can be solved easily by solving for z in the second equation and substituting into the first equation.
You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".
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From second equation: y = 8 + 2xSubstitute for y in first equation: 3x + 16 + 4x = 2ie 7x = -14ie x = -2 and y = 4
From first equation: y = 5 - 5xSubstitute for y in second equation: 3x + 10 - 10x = 3ie -7x = -7ie x = 1 and y = 0
If you multiply each term of the first type of equation by a common multiple of all the denominators then you will have an equation of the second type.For example, if you have 2/3*y = 4/5*x + 7/9 then multiplying by the LCM of 3, 5, 9) = 45, gives30*y = 39*x + 35: all integers!
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.