What is the solution of the system of equations?

y = -3x + 7

y = 2x - 8

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What is the solution of the system of equations?

y = -3x + 7

y = 2x - 8

y = -2

x = 3

Step-by-step explanation:

Solve using elimination

1. Rearrange the equations to make it easier to solve

y = -3x + 7 → 3x + y = 7

y = 2x - 8 → 2x - y = 8

2. Multiply the equations to have a matching coefficient

2(3x + y = 7) = 6x + 2y = 14

3(2x - y = 8) = 6x - 3y = 24

3. Subtract

6x + 2y = 14

- 6x - 3y = 24

0 + 5y = -10

4. Solve for y

5y = -10

y = -2

5. Substitute y in any equation to solve for x

-2 = -3x + 7

-3x = -9

x = 3

x = 3, y = -2

Step-by-step explanation:

Since y=y

then, -3x +7 = 2x-8

7+8 = 3x+2x

15 = 5x

x=3

substitute

y = 2(3) - 8

y = -2

Hope that helped!!! k

1) y = -8/5x + 8

2) slope = -3

3) x = 4

4) x ≥ 22/3

5) x = 21/16

6) x = 12

Step-by-step explanation:

1) For the slope, you know you go up 8 left 5 to get from the x-intercept to your y-intercept so it’s positive 8 over -5 (rise over run).

This makes your slope 8/-5 which is the same as -8/5

2) The slope is next to the x, so the slope is -3/1 which is -3.

3) Rearrange the equation to y = mx + b.

Firstly, subtract 6x from both sides:

-3y = -6x + 24

Then, divide both sides by -3:

y = 2x - 8

To get the x-intercept, divide the y-intercept (but positive) by the slope.

8/2 = 4

Your x-intercept is 4.

4) Distribute on the terms:

-53 ≥ -9x - 9 + 3x

Combine like terms:

-53 ≥ -6x - 9

Add 9 to both sides:

-44 ≥ -6x

Divide both sides by -6:

44/6 ≤ x

(Inequality flipped because you divide by a negative)

Simplify:

22/3 ≤ x

Flip the inequality:

x ≥ 22/3

5) Multiply both sides by 4:

3x - x/3 = 7/2

Multiply both sides by 3:

9x - x = 21/2

Combine like terms:

8x = 21/2

Divide both sides by 8:

x = 21/16

or

x = 1.3125

6) Combine like terms:

7x + 6 = 90

Subtract 6 from both sides:

7x = 84

Divide both sides by 7:

x = 12

Hope this helps!

D

Step-by-step explanation:

Slope is 'm' in y = mx + c

m is the coefficient of x

So, m = -3

(4, -5)

Step-by-step explanation:

we know that

If a ordered pair lie on the line, then the ordered pair must satisfy the equation of the line

we have

[tex]y=-3x+7[/tex]

Verify each ordered pair

case 1) (4, -5)

substitute the value of x and the value of y in the linear equation and then compare the results

[tex]-5=-3(4)+7[/tex]

[tex]-5=-5[/tex] ---> is true

so

The ordered pair satisfy the linear equation

therefore'

The ordered pair lie on the line

case 2) (4, 19)

substitute the value of x and the value of y in the linear equation and then compare the results

[tex]19=-3(4)+7[/tex]

[tex]19=-5[/tex] ---> is not true

so

The ordered pair not satisfy the linear equation

therefore'

The ordered pair not lie on the line

case 3) (1,5)

substitute the value of x and the value of y in the linear equation and then compare the results

[tex]5=-3(1)+7[/tex]

[tex]5=4[/tex] ---> is not true

so

The ordered pair not satisfy the linear equation

therefore'

The ordered pair not lie on the line

case 4) (1,-19)

substitute the value of x and the value of y in the linear equation and then compare the results

[tex]-19=-3(1)+7[/tex]

[tex]-19=4[/tex] ---> is not true

so

The ordered pair not satisfy the linear equation

therefore'

The ordered pair not lie on the line

1/3

Step-by-step explanation:

Perpendicular lines have a slope that is the opposite reciprocal of the original line slope. To find it, first flip the fraction (-3 to -1/3). Then, add/get rid of the negative sign based on if it was there in the first place (-1/3 to 1/3). Thus, the slope would be 1/3.

Hope this helped 🙂

d

Step-by-step explanation:

1.（A）Ithink it is the option a, because b,c,d cannot be equaled to that equation

-3

Step-by-step explanation:

the coefficient of the x term is the slope in any equation that is in slope intercept form

The equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .

The solution of the system is (3,6).

Step-by-step explanation:

Linear equation: [tex]y=mx+c[/tex] , where m= slope

c = y-intercept.

In the first table, the y-intercept = 5 [ y-intercept = value of y at x=0.

Slope for first table = [tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{6-5}{3-0}=\dfrac{1}{3}[/tex]

The equation that represents the first table:

[tex]y=\dfrac{1}{3}x+5[/tex]

So, the equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .

Also, the solution of the system is the common point (x,y) that satisfy both equations in the system.

Here, x=3 and y=6 is the common value in both tables.

So, the solution of the system is (3,6).