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Introduction: Systems of Linear Equations - Part 1

12Elimination by equating coefficients (2/2)

Solve the first equation for xx .

2x+1\displaystyle 2x+1==−32x+92\displaystyle -\frac{3}{2}x+\frac{9}{2}+32x\displaystyle +\frac{3}{2}x
72x+1\displaystyle \frac{7}{2}x+1==92\displaystyle \frac{9}{2}−1\displaystyle -1
72x+1\displaystyle \frac{7}{2}x+1==27\displaystyle \frac{2}{7}⋅27\displaystyle \cdot\frac{2}{7}
x\displaystyle x==1\displaystyle 1

Plug that xx into one of both equations

To demonstrate that it really doesn't matter which of the two equations you use, here are both equations.

y=2⋅1+1\color{#FF6600}y = 2 \cdot \color{#660099}{1} +1

y=3\color{#FF6600}y = 3

y=−32⋅1+92\color{#FF6600}y = -\frac{3}{2} \cdot \color{#660099}{1} + \frac{9}{2}

y=3\color{#FF6600}y = 3

So the intersection point of both lines is P(1∣3)P(\color{#660099}{1}|\color{#FF6600}3)!


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