Question

A system of equations consists of a line s of the equation y = x - 5 that is graphed in orange, and a line t that passes through the points (0, 2) and (8, -4). The equation of line t is y = −3 4 x + 2. What is the solution to this system of linear equations?

Answer 1

ANSWER

$x = 4$

and

$y = - 1$

EXPLANATION

Line s has equation:

y=x-5

And line t has equation:

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

We equate the two equations to get:

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

Multiply through by 4

$4x - 20 = - \frac{3}{4} x \times 4 + 2 \times 4$

$4x - 20 = - 3 x + 8$

$4x + 3x = 8 + 20$

7x=28

$x = \frac{28}{7} = 4$

$y = 4 - 5 = - 1$

Answer 2

Answer:

(4, -1) is the solution of the system of equations.

Step-by-step explanation:

A system of equations consists of a line y = x - 5 and a line passing through two points (0, 2) and (8, -4)

And the equation of that passes through these points will be $y=-\frac{3}{4}x+2$

Now we have to find the solution of the system of linear equations.

By equating both the equations

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

Now we multiply this equation by 4

4(x - 5) = -3x + 4×2

4x - 20 = -3x + 8

4x + 3x = 8 + 20

7x = 28

x = 4

Now we put x = 4 in the equation y = x - 5

y = 4 -5

y = -1

Therefore, (4, -1) is the solution of the system of equations.