3. Solve the following system of equations by
and check your answer
Graph both equations. Solve the equations for y. In the first one
transpose the x term
and divide both sides by 3.
Do the same thing for the other equation
Transpose
and divide by 2.
Now make up tables of x's and y's for both equations.
plot the points and draw the graphs. We see that the point of
intersection is (3, -1), so the solution is
and
If we substitute these numbers into the original equations, in
the first equation we get
2(3) + 3(-1) = 3
or
6 - 3 = 3
and in the second equation we get
3(3) + 2(-1) = 7
or
9 - 2 = 7
and the numbers check in both equations.
b. Substitution
Solve one of the equations for one of the unknowns. In this
case it is easiest to solve the first equation for y.
Now substitute this solution into the other equation.
Remove parentheses
At this point we could combine the x terms. To subtract the
coefficients, 3 - 4/3 = 5/3, but it might be easier to first clear
denominators by multiplying both sides of the equation by 3.
To find y, substitute this solution into the equation where we
solved for y as a function of x
Multiply the equations by suitable numbers so that the
coefficients on one of the unknowns match up. In this case, if we
multiply the first equation by 3 and the second equation by -2, the
coefficients of the x's will match up and they will go away when we
add.
To find x, we substitute this value of y into either of the
original equations. The first equation might be easiest.
