Q12. - Algebra 2

Question

Solve each system of equations by graphing.

$\begin{array}{c}12.8x-10y=7\\ 4x-5y=7\end{array}$

Step-by-Step Solution

Answer

The system of equations is inconsistent. There is no point such that it satisfy the system of equations.

Step-1 – Apply the concept of slope-intercept form

Equation of line in slope intercept form is expressed below.

$y=mx+c$

Where m is the slope and c is the intercept of y-axis.

Step-2 –Write the equations in slope-intercept form

Consider the first equation $8x-10y=7$. 

Rewrite the equation in form of slope-intercept form.

Subtract both sides by $8x$ and then divide by $-10$.

$\begin{array}{c}8x-10y-8x=7-8x\\ -10y=7-8x\\ y=\frac{8}{10}x-\frac{7}{10}\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $\frac{8}{10}$ and intercept of y-axis c is $-\frac{7}{10}$.

Now, consider the second equation $-\frac{7}{10}$. 

Rewrite the equation in form of slope-intercept form.

Subtract both sides by $4x$ and then divide by $-5$.

$\begin{array}{c}4x-5y=7\\ -5y=7-4x\\ -5y=-4x+7\\ y=\frac{4}{5}x-\frac{7}{5}\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $\frac{4}{5}$ and intercept of y-axis c is $-\frac{7}{5}$.

Step-3 – Identify the point of intersection of the equations

Plot the equations on the same plane and the point where both the equations intersect is the solution of the system of the equations.

The red line denotes the equation $8x-10y=7$ and blue line denotes the equation $4x-5y=7$.

There is no point of intersection.

The lines are parallel as they do not intersect each other. There is no point such that it satisfy the system of equations. There is no solution to system of equations. Hence, the system of equations is inconsistent.