Question

Solve the system of linear equations:16x+17y=1 12x−15y=1 x= y=

Answer 1

We will use the elimination method to solve that system:

Let's look at the denominators of the coefficients for the x variable, in this case we have 2 and 6, lets convert the second equation to have 1/6 as coefficient, so:

$\frac{1}{2}x-\frac{1}{5}y=1$$\frac{1}{2}x\cdot\frac{1}{3}-\frac{1}{5}y\cdot\frac{1}{3}=1\cdot\frac{1}{3}$$\frac{1}{6}x-\frac{1}{15}y=\frac{1}{3}$

We already have the same coefficient, now we are going to subtract:

$\frac{22}{105}y=\frac{2}{3}$$y=\frac{105\cdot2}{22\cdot3}$$y=\frac{210}{66}=\frac{105}{33}=\frac{35}{11}$

We already have the value of y, now we can find the value of x by substituting in any of the equations, let's use the second one:

$\frac{1}{2}x-\frac{1}{5}y=1$$\frac{1}{2}x-\frac{1}{5}\cdot\frac{35}{11}=1$$\frac{1}{2}x-\frac{35}{55}=1$$\frac{1}{2}x-\frac{7}{11}=1$$\frac{1}{2}x=1+\frac{7}{11}$$\frac{1}{2}x=\frac{18}{11}$$x=\frac{18\cdot2}{11}$$x=\frac{36}{11}$