Question

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 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)

Answer 1

Answer:

Question 1. (2.2, -1.4)

Question 2. (1.33, 1)

Step-by-step explanation:

Equations for the given lines are

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

It is given that this line passes through two points (0, 2.5) and (2.2, 1.4).

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

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

Now we have to find a common point through which these lines pass or solution of these equations.

From equations (1) and (2),

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

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

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

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

x = 2.2

From equation (2),

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

y = -1.4

Therefore, solution of these equations is (2.2, -1.4).

Question 2.

The given equations are y = 1.5x - 1 and y = 1

From these equations,

1 = 1.5x - 1

1.5x = 2

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

Therefore, the solution of the system of linear equations is (1.33, 1).

Answer 2

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Step-by-step explanation:

Question 1)

Two lines, with their corresponding equations are given and we have to find the solution to the system of equations.

The given lines are:

Equation of Line 1:

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

This line passes through the points: (0, 2.5) , (2.2, -1.4)

Equation of Line 2:

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

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

By looking at the graph/given data we have to find the solution of these linear equations.

Remember that the solution of linear equations is an ordered pair, through which both the lines pass i.e. the point at which both the given lines intersect is the solution of the linear equations.

From the given data we can see that both the lines pass through one common point, (2.2, -1.4). Since, both lines pass through this point, this means this is the point of intersection of the lines and hence there solution.

So, the answer to this questions is (2.2, -1.4)

Question 2)

The given equations are:

y = 1.5x - 1                                        Equation 1

y = 1                                                  Equation 2

We can solve these equations by method of substitution.

Substituting the value of y from Equation 2, in Equation 1, we get:

1 = 1.5x - 1

1 + 1 = 1.5x

2 = 1.5x

x = 2/1.5

x = 1.33

y = 1

Thus, the solution of the given linear equations is (1.33, 1)