Solve each word problem using a system of equations. use substitution or elimination.
1. one number added to three times another number is 24. five times the first number added to
three times the other number is 36. find the numbers.

Answers

y = x + 4

3x - 2y = -7

We can substitute the first equation into the second

3x - 2(x + 4) = -7

3x - 2x - 8 = -7

x - 8 = -7

x = 1

y = 1 + 4

y = 5

So, the answer is (1, 5)

x=-7/2, y=1

Step-by-step explanation:

y=-2x-6

y=x+9

I'm going to use elimination.

2y=2x+9

y=-2x-6

3y=3

y=1

Enter y into one of the equations to find x.

2=2x+9

2x=-9+2

2x=-7

x=-7/2

A. The solution is (0.9,-0.7)

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

( 0.9 ,− 0.7 )

Equation Form:

x  =  0.9  & y  =  − 0.7

a. (0.1,0.4)

Step-by-step explanation:

(1,5)

Step-by-step explanation:

Use substitution, and plug the first equation into the 2nd one:

3x-2(x+4)=-7 -->

3x-2x-8 = -7 -->

x - 8 = -7

x = 1

Plug this into the first equation:

y = 1 + 4

y = 5

(1,5)

(-2,-4)

Step-by-step explanation:

2x-y=0

-2(x+3y=-14)

-2x-6y=28

x terms cancel

-y+-12y=-13y

0+28=28

-7y=28

28/-7

y=-4

plug into the orginal equation

2x-(-4)=0

simply: 2x+4=0

elimante the 4

2x=-4

divide by 2

x=-2

A. The unique solution to the system is (0.1,0.4)

Step-by-step explanation:

 You can follow these steps to solve the system of equation by the Elimination Method:

- Multiply the first equation by -0.7, then add both equations and solve for "y":

\left \{ {-0.7(x + y) =-0.7(0.5)} \atop {0.7x + 0.6y = 0.31}} \right.\\\\\left \{ {-0.7x-0.7y =-0.35} \atop {0.7x + 0.6y = 0.31}} \right.\\............................\\-0.1y=-0.04\\\\y=0.4

- Substitute the value of "y" into any original equation to find the value of "x". Then:

x + (0.4) = 0.5\\\\x=0.5-0.4\\\\x=0.1

 Therefore, the unique solution to the system is (0.1,0.4)

A. The unique solution to the system is (0.9,-0.7)

Step-by-step explanation:

 You can follow these steps to solve the system of equation by the Elimination Method:

- Multiply the first equation by 0.5, then add both equations and solve for "y":

\left \{ {{0.5(x + y) = 0.5(0.2)} \atop {-0.5x + 0.7y = -0.94}} \right.\\\\\left \{ {{0.5x + 0.5y = 0.1} \atop {-0.5x + 0.7y = -0.94}} \right.\\...............................\\1.2y=-0.84\\y=-0.7

- Substitute the value of "y" into any original equation to find the value of "x". Then:

x + (-0.7) = 0.2\\\\x=0.2+0.7\\\\x=0.9

 Therefore, the unique solution to the system is (0.9,-0.7)

Step-by-step explanation:

x + 3y = 24multiply by -1

5x + 3y = 36

-x - 3y = -24 (result of multiplying by -1)

5x + 3y = 36

add

4x = 12

x = 12/4

x = 3 <

x + 3y = 24

3 + 3y = 24

3y = 24 - 3

3y = 21

y = 21/3

y = 7 <

Step-by-step explanation:

x + 3y = 24multiply by -1

5x + 3y = 36

-x - 3y = -24 (result of multiplying by -1)

5x + 3y = 36

add

4x = 12

x = 12/4

x = 3 <

x + 3y = 24

3 + 3y = 24

3y = 24 - 3

3y = 21

y = 21/3

y = 7 <



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