Question

Solve the following system of equations by graphing and select the correct answer below:

4x + 3y = 29
2x − 3y = 1

a) x = 3, y = 5
b) x = −3, y = 5
c)x = 5, y = 3
d) x = 5, y = −3

Answer 1

c)x = 5, y = 3

EXPLANATION

The given system has equations:

`4x + 3y = 29`

and

`2x - 3y = 1`

We graph the above equations using a graphing software to obtain the graph shown in the attachment.

The solution to the given system is the point of intersection of the two straight lines.

From the graph, the two straight lines intersected at (5,3).

This implies that the solution to the system is:

`x = 5 \: and \: y = 3`

The correct answer is option is C

Answer 2

Answer: option c

Explanation:

Find the x-intercept and y-intercept of each line.

To find the x-intercept, substitute
`y=0` into the equation and solve for "x".

To find the y-intercept, substitute
`x=0` into the equation and solve for "y".

- For the first equation:

x-intercept

`4x + 3y = 29\\\\4x + 3(0)= 29\\\\4x=29\\\\x=(29)/(4)\\\\x=7.25`

y-intercept

`4x + 3y = 29\\\\4(0) + 3y = 29\\\\3y=29\\\\y=(29)/(3)\\\\y=9.66`

Graph a line that passes through the points (7.25, 0) and (0, 9.66)

- For the second equation:

x-intercept

`2x - 3y = 1 \\\\2x - 3(0) = 1 \\\\2x=1\\\\x=0.5`

y-intercept

`2x - 3y = 1\\\\2(0) - 3y = 1\\\\-3y=1\\\\y=-0.33`

Graph a line that passes through the points (0.5, 0) and (0, -0.33)

Observe the graph attached. You can see that point of intersection of the lines is (5,3); then this is the solution of the system. Therefore:

`x=5\\y=3`