Question

Find the solution to the system of equations. Write the solution as an ordered pair. If there are no solutions, write 'no solutions'. If there are infinitely many, write 'infinitely many'.

y = −7/2x + 11

7x + 2y = 20

Answer 1

We can solve this system of equations by using the substitution method. To use substitution, we'll solve one equation for one variable and substitute that into the other equation.

First, we'll solve the equation y = -7/2x + 11 for x:
x = (y - 11) / (-7/2)

Now we'll substitute that expression into the other equation, 7x + 2y = 20:
(7(y - 11) / (-7/2)) + 2y = 20

we can simplify and solve for the y:
y = -14/3

Now we can substitute this y-value back into the first equation to find the x-value:
x = (y - 11) / (-7/2) = (-14/3 - 11) / (-7/2) = -5/3

So the solution of the system of equations is (-5/3,-14/3) which is the ordered pair (x,y).