Question

Billy graphed the system of linear equations to find an approximate solution. y = A system of equations. y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction. y equals StartFraction 3 over 4 EndFraction x minus 3.x + y = x – 3 A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction and passes through the (0, 2.5) and (2.2, negative 1.4). The second line is labeled y equals StartFraction 3 over 4 EndFraction x minus 3 and passes through (0, negative 3, 0.14) and (2.2, negative 1.4) Which points are possible approximations for this system? Select two options. (1.9, 2.5) (2.2, –1.4) (2.2, –1.35) (1.9, 2,2) (1.9, 1.5) Mark this and return

Answer 1

Explanation:

To find possible approximations for the system of linear equations, we need to look for points that satisfy both equations. Let's check the given points:

(1.9, 2.5):

For the first equation:

y = -7/4 * x + 5/2

y = -7/4 * 1.9 + 5/2 ≈ -1.225 + 2.5 ≈ 1.275

For the second equation:

y = 3/4 * x - 3

y = 3/4 * 1.9 - 3 ≈ 1.425 - 3 ≈ -1.575

The point (1.9, 2.5) does not satisfy either equation.

(2.2, -1.4):

For the first equation:

y = -7/4 * x + 5/2

y = -7/4 * 2.2 + 5/2 ≈ -3.85 + 2.5 ≈ -1.35

For the second equation:

y = 3/4 * x - 3

y = 3/4 * 2.2 - 3 ≈ 1.65 - 3 ≈ -1.35

The point (2.2, -1.4) satisfies both equations.

(2.2, -1.35):

For the first equation:

y = -7/4 * x + 5/2

y = -7/4 * 2.2 + 5/2 ≈ -3.85 + 2.5 ≈ -1.35

For the second equation:

y = 3/4 * x - 3

y = 3/4 * 2.2 - 3 ≈ 1.65 - 3 ≈ -1.35

The point (2.2, -1.35) satisfies both equations.

(1.9, 2.2):

For the first equation:

y = -7/4 * x + 5/2

y = -7/4 * 1.9 + 5/2 ≈ -1.225 + 2.5 ≈ 1.275

For the second equation:

y = 3/4 * x - 3

y = 3/4 * 1.9 - 3 ≈ 1.425 - 3 ≈ -1.575

The point (1.9, 2.2) does not satisfy either equation.

(1.9, 1.5):

For the first equation:

y = -7/4 * x + 5/2

y = -7/4 * 1.9 + 5/2 ≈ -1.225 + 2.5 ≈ 1.275

For the second equation:

y = 3/4 * x - 3

y = 3/4 * 1.9 - 3 ≈ 1.425 - 3 ≈ -1.575

The point (1.9, 1.5) does not satisfy either equation.

The two possible approximations for this system are (2.2, -1.4) and (2.2, -1.35).