Question

HELP ASAP MY PARENTS ARE COUNTING ON ME

The system of linear equations 3x + 2y = −6 and y equals one half times x plus 4 is graphed on a coordinate plane. Approximate the solution to the system.

coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma negative 3 and negative 2 comma 0

(−3.5, 1.25)
(−3.5, 2.25)
(1.5, 4.25)
(1.5, −5.25)

Answer 1

An answer is an option (C) (1.5, 4.25).

Explanation:

# Approximating Solution to a System of Linear Equations

The given system of linear equations is:

3x + 2y = −6 ...(1)

y = 1/2 x + 4 ...(2)

The solution to the system can be approximated by graphing the two equations on a coordinate plane and finding the point of intersection of the two lines.

The first equation can be written in a slope-intercept form:

2y = -3x - 6

y = (-3/2)x - 3

Plotting this on the coordinate plane, we get a line passing through the points (0,-3) and (-2,0).

The second equation can be written in a slope-intercept form:

y = (1/2)x + 4

Plotting this on the coordinate plane, we get a line passing through the points (0,4) and (2,5).

The two lines intersect at approximately (1.5, 4.25). Therefore, the solution to the system is as follows:

x ≈ 1.5

y ≈ 4.25

Hence, the answer is an option (C) (1.5, 4.25).

Answer 2

An answer is an option (C) (1.5, 4.25).

Explanation:

# Approximating Solution to a System of Linear Equations

The given system of linear equations is:

3x + 2y = −6 ...(1)

y = 1/2 x + 4 ...(2)

The solution to the system can be approximated by graphing the two equations on a coordinate plane and finding the point of intersection of the two lines.

The first equation can be written in a slope-intercept form:

2y = -3x - 6

y = (-3/2)x - 3

Plotting this on the coordinate plane, we get a line passing through the points (0,-3) and (-2,0).

The second equation can be written in a slope-intercept form:

y = (1/2)x + 4

Plotting this on the coordinate plane, we get a line passing through the points (0,4) and (2,5).

The two lines intersect at approximately (1.5, 4.25). Therefore, the solution to the system is as follows:

x ≈ 1.5

y ≈ 4.25

Hence, the answer is an option (C) (1.5, 4.25).