A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFract

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A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFract

ion 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 is the best approximate solution of the system of linear equations y = 1.5x – 1 and y = 1? (0.33, 1) (1.33, 1) (1.83, 1) (2.33, 1)

Mathematics

2 answers:

AnnZ [12.3K] · Answer 1 · 2026-02-19T18:39:42+03:00

Answer:

Question 1: (2.2, -1.4)

Question 2: (1.33, 1)

Detailed solution:

The equations corresponding to the provided lines are:

$y=-\frac{7}{4}x+\frac{5}{2}$ -----(1)

This line crosses through points (0, 2.5) and (2.2, -1.4).

$y=\frac{3}{4}x-3$ ------(2)

This line passes through points (0, -3) and (2.2, -1.4).

The objective is to determine the common coordinate point for both lines, i.e., solve the equations simultaneously.

From equations (1) and (2),

$-\frac{7}{4}x+\frac{5}{2}=\frac{3}{4}x-3$

$x(\frac{7}{4}+\frac{3}{4})=\frac{5}{2}+3$

$\frac{10}{4}x=\frac{11}{2}$

Simplifying gives:

x = $\frac{11}{2\times 2.5}$

which is x = 2.2

Substituting x into equation (2),

$y=\frac{3}{4}\times (2.2)-3$

y = -1.4

Hence, the solution to these equations is (2.2, -1.4).

Question 2.

The given system is y = 1.5x - 1 and y = 1.

Setting y equal,

1 = 1.5x - 1

Add 1 to both sides:

1.5x = 2

Divide both sides by 1.5:

x = $\frac{2}{1.5}=1.33$

Therefore, the solution to the system is (1.33, 1).

AnnZ [12.3K] · Answer 2 · 2026-02-19T18:37:28+03:00

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Detailed solution:

Question 1)

We are provided with two linear equations representing lines, and we need to find the intersection point that solves the system.

The lines given are:

Line 1 equation:

$y=\frac{-7}{4}x+\frac{5}{2}$

This line passes through points (0, 2.5) and (2.2, -1.4).

Line 2 equation:

$y=\frac{3}{4}x-3$

The second line goes through (0, -3) and (2.2, -1.4).

According to the graph and data, the solution to the system is the coordinate where both lines intersect.

The solution to a system of linear equations is the coordinate pair common to both lines, i.e., the intersection point.

Here, both lines share the point (2.2, -1.4), indicating it is their intersection and the solution.

Therefore, the solution for question 1 is (2.2, -1.4).

Question 2)

The equations given are:

y = 1.5x - 1 Equation 1

y = 1 Equation 2

The method of substitution can be used to find the solution.

Replacing y from Equation 2 into Equation 1 gives:

1 = 1.5x - 1

Add 1 to both sides:

2 = 1.5x

Dividing both sides by 1.5 yields:

x = 2/1.5

x = 1.33

y = 1

Thus, the solution of the system is (1.33, 1).