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# Solve a linear system using algebra: substitution

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1. 8a-3b=-4

a=5-2b

2. 2x-3y=1

x=y+1

3. 2x+y=5

x-3y=13

Guest Mar 2, 2017
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#1
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1. 8a-3b=-4

a=5-2b

You know that a equals 5-2x so put this in brackedts and sub it into your first equation.

$$8a-3b=-4 \qquad (1)\\ a=(5-2b)\qquad (2)\\~\\ 8(5-2b)-3b=-4 \\ \text{now solve it for b}\\ 40-16b-3b=-4\\ 40-19b=-4\\ 40-19b-40=-4-40\\ 19b=-44\\ b=\frac{-44}{19}\\ b=-2\frac{6}{19}\\~\\ \text{Now sub this value of b into (2)}\\ a=5-2*\frac{-44}{19}\\ a=5+\frac{88}{19}\\ a=5+4\frac{12}{88}\\ a=9\frac{3}{22}\\ so\\ b=-2\frac{6}{19}\qquad and \qquad a=9\frac{3}{22}\\$$

You can do ther others by copying this one. :)

Melody  Mar 2, 2017

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