# Solve For Y Problems

Solving for two variables (normally denoted as "x" and "y") requires two sets of equations.

Solving for two variables (normally denoted as "x" and "y") requires two sets of equations.

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If you multiply the second equation by −4, when you add both equations the y variables will add up to 0. Instead of multiplying one equation in order to eliminate a variable when the equations were added, you could have multiplied both equations by different numbers. Adding 4x to both sides of Equation A will not change the value of the equation, but it will not help eliminate either of the variables—you will end up with the rewritten equation 7y = 5 4x.

The correct answer is to add Equation A and Equation B. Multiplying Equation A by 5 yields 35y − 20x = 25, which does not help you eliminate any of the variables in the system.

And since x y = 8, you are adding the same value to each side of the first equation.

If you add the equations above, or add the opposite of one of the equations, you will get an equation that still has two variables.

One cannot, the system of equations have no solution.

One may also arrive at the correct answer with the help of the elimination method (also called the addition method or the linear combination method) or the substitution method.

For whatever reason, there are different formats for simple linear equations.

I prefer the slope-intercept form; at times, the point-slope form is helpful; some textbooks strongly prefer what they sometimes call the "intercept" form, which is often (though not always) given as being " From what I've learned about slope, I know that parallel lines have the same slope, and perpendicular lines have slopes which are negative reciprocals (that is, which have opposite signs and which are flipped fractions of each other). These slopes have opposite signs, so their lines are not parallel.

When using the substitution method we use the fact that if two expressions y and x are of equal value x=y, then x may replace y or vice versa in another expression without changing the value of the expression.

Example Solve the systems of equations using the substitution method $$\left\{\begin y=2x 4\ y=3x 2\ \end\right.$$ We substitute the y in the top equation with the expression for the second equation: $$\begin 2x 4 & = & 3x 2\ 4-2 & = & 3x-2x\ 2 & = & x\ \end$$ To determine the -value in any of the equations.

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