4. Solve the following system of equations by
and check your answer
Solve each equation for y. With the first equation
transpose the x term,
and divide by the coefficient of y.
With the other equation,
transpose the x term,
and divide by the coefficient of the y.
Now graph both equations in the same graph.
We can see that the x coordinate is somewhere around 2, and
the y coordinate is between 0 and -1. But we will need to use other,
computational methods to be more precise.
Solve one of the equations for one of the unknowns. It would
be best to solve the first equation for y for two reasons. Most
importantly, if we solve the first equation for y, we will have fewer
fractions to work with. The other reason is that we have already
solved the first equation for y in the process of graphing.
Now substitute this solution in for y in the other equation.
This gives us an equation with only one unknown. We can solve
this equation. Remove parentheses.
Clear denominators. Multiply both sides by 3.
or
Combine the x terms and transpose the 6.
or
Divide both sides by 13.
or
which, as we suspected, is very close to 2.
To find y, the simplest way would be to substitute this solution
into the equation where y is expressed as a function of x.
After simplifying, find common denominators.
or
which is also about what we expected.
If we substitute these values in the first equation,
we get
or
which checks.
The other equation
becomes
and they both check.
Addition
In order to get the coefficients of the y terms to match up, we
could multiply the top equation by 2 and the other equation by -3.
and we get
To find y, we substitute this solution into either of the original
equations. If we substitute this into the first equation, we get
and solve for y.
Simplify.
transpose the 54/13 to the other side of the equation and find
common denominators.
or
Divide both sides by 3.
and we get the same answer as before.