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true
The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.
You cannot work a simultaneous equation. You require a system of equations. How you solve them depends on their nature: two or more linear equations are relatively easy to solve by eliminating variables - one at a time and then substituting these values in the earlier equations. For systems of equations containing non-linear equations it is simpler to substitute for variable expression for one of the variables at the start and working towards the other variable(s).
To solve two simultaneous equations - usually two equations with the same two variables each - you can use a variety of techniques. Sometimes you can multiply one of the two equations by a constant, then add the two equations together, to get a resulting equation that has only one variable. Sometimes you can solve one of the equations for one variable, and replace this variable in the other equation. Once again, this should give you one equation with a single variable to be useful.
The substitution method in mathematics is a technique used to solve systems of equations by isolating one variable and substituting it into the other equation. The method is not attributed to a single inventor, as it has been used by mathematicians for centuries. The concept of substitution in algebra can be traced back to ancient civilizations such as the Babylonians and Greeks, who used similar methods to solve mathematical problems.
true
true
true
The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.
You cannot work a simultaneous equation. You require a system of equations. How you solve them depends on their nature: two or more linear equations are relatively easy to solve by eliminating variables - one at a time and then substituting these values in the earlier equations. For systems of equations containing non-linear equations it is simpler to substitute for variable expression for one of the variables at the start and working towards the other variable(s).
To solve two simultaneous equations - usually two equations with the same two variables each - you can use a variety of techniques. Sometimes you can multiply one of the two equations by a constant, then add the two equations together, to get a resulting equation that has only one variable. Sometimes you can solve one of the equations for one variable, and replace this variable in the other equation. Once again, this should give you one equation with a single variable to be useful.
The substitution method in mathematics is a technique used to solve systems of equations by isolating one variable and substituting it into the other equation. The method is not attributed to a single inventor, as it has been used by mathematicians for centuries. The concept of substitution in algebra can be traced back to ancient civilizations such as the Babylonians and Greeks, who used similar methods to solve mathematical problems.
To determine that the value of ( d ) is the same in both equations, you can isolate ( d ) in each equation and compare the resulting expressions. If both equations yield the same expression for ( d ) when simplified, then the value is confirmed to be the same. Additionally, substituting known values from either equation should yield consistent results for ( d ).
(a) rearrange one of the equations so that x or y is alone on one side of the equals sign.
You can't. Math is not an algebraic expression. Simplifying an equation, however, can take multiple forms. Sometimes simplify simply means to solve an equation. Other times, it can mean to bring an equation into a standard form, such as with line equations, or quadratic equations.
To solve one-variable equations, isolate the variable on one side of the equation using algebraic operations. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same number, ensuring to maintain the equality. Simplify both sides as needed, and check your solution by substituting it back into the original equation to verify that both sides are equal.
You can easily tell by substituting 0 for a.