Question

For each part, solve the system of linear equations, or show that no real solution exists. Graphically support your answer. 4x+2y=9 ; x+y=3

Answer 1

the solution is the point (3/2, 3/2)

Explanation:

Hi there!

We have the following system of linear equations:

4x + 2y = 9

x + y = 3

Let´s write the equations in terms of y in function of x:

4x + 2y = 9

subtract 4x from both sides of the equation

2y = 9 - 4x

Divide by 2 both sides of the equation

y = 9/2 - 2x

Now for the other equation:

x + y = 3

y = 3 - x

Let´s equalize both expresions and solve the resulting equation for x:

3 -x = 9/2 - 2x

add 2x and subtract 3 from both sides of the equation

2x - x = 9/2 - 3

x = 3/2

Now let´s find y:

y = 3-x

y = 3 - 3/2 = 3/2

Then, the solution is the point (3/2, 3/2)

Please, see the attached figure for corroboration.