11.4 solving linear systems by multiplying first homework answer key

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Module 11.4Solving Linear SystemsBy Multiplying FirstHow can you solve a system of linear equationsby using multiplication and elimination?P. 515

What do you do if all 4 variables have coefficients, and none can be eliminated?For example:?? + ?? = ??? − ?? = −??The first term of both equations,3xand2x, can’t be added together, even if you multiply one of them by –1.The second term of both equations,8yand–2y, can’t be added together.But–we can multiply ONE ENTIRE equation by a number,which will make one of the coefficients become an opposite.Specifically: If we multiply the whole 2ndequation by4, here’s what it becomes:??? − ?? = −??⇒??− ??= −??Did you notice that the new 2ndterm,−??, is the opposite of the 2ndterm of the 1stequation,???Here’s how they line up:?? + ?? = ??? − ?? = −??Now you can add the 2ndterms!

P. 519Solving Systems of Equations by Multiplying FirstStep 1Decide which variable to eliminate.Step 2Multiply one or both equations by a constant so that adding the equations will eliminate the variable.

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How do you solve a system of equations by multiplying?

How can you decide whether to add or subtract to eliminate a variable in a linear system?