4. Solve the following system of equations by
and check your answer
a) Graphing
Solve each equation for y. For the first one,
first, transpose the x term to the other side of the equation.
We do the same thing with the other equation.
but here we also have a coefficient to remove.
Divide both sides by -2.
Make up a table of x's and y' for each equation, and graph them
both.
and we see that the solution is x = -1 and y = 3.
if we substitute these numbers into the first equation, we get
which checks.
In the second equation we get
so they check in both equations
Solve one of the equations for one of the unknowns. In this
case, it would be best to solve the second equation for x.
Substitute this solution into the other equation
This gives us an equation with only one unknown. Solve this
equation. First, remove parentheses.
Combine the y terms on the left and transpose the -14 to the
other side.
or
Divide both sides by 5.
To find x, substitute this solution into the equation where we
had solved for x as a function of y,
and get
or
which is the same solution as we got before.
Multiply the equations by suitable numbers so that the
coefficients of the y terms match up. In this case we could simply
multiply the top equation by 2.
or
To solve for y, substitute this solution into either of the original
equations and solve for y. The best equation would be the first one
or
so all we have to do to solve for y is to add 2 to both sides.