Question

Solve the system algebraically. Check your work. 4x + 5y = 12 7x + 5y = 6 Make sure there are NO SPACES in your answer. Be sure to include a comma between the x and y values.

Answer 1

(-2,4)

EXPLANATION

The given equations are:

4x + 5y = 12

7x + 5y = 6

Subtract the first equation from the second equation.

7x-4x+5y-5y=6-12

3x=-6

Divide both sides by 3 to obtain:

x=-2

Put x=-2 into the first equation to get:

4(-2)+5y=12

-8+5y=12

5y=12+8

5y=20

y=20/5

y=4

Checking

4(-2)+5(4)=12

-8+20=12

12=12

Also

7(-2)+5(4)=6

-14+20=6

6=6

Answer 2

The solution is (-2,4)

Explanation:

* Lets revise how to solve the system of equations algebraically

- If the system of equation is ax+by=c and dx+ey=f, then we can use

the elimination method to solve

- The steps of the elimination method

# Change the coefficient of one variable in one of the two equation

to have the same coefficient with opposite sign of this variable in the

second equation (a = -d)

# Add the two equations to eliminate this variable (by+ey=c+f)

# Solve to find the second variable (y=(c+f)/(b+e))

# Substitute the the value of the second variable in any equation to

find the first variable

* Now lets solve the problem

∵ 4x+5y=12 ⇒ (1)

∵ 7x+5y=6 ⇒ (2)

- The variable y has the same coefficient in the two equations, then

eliminate it by multiply one of the equation by -1 to make

opposite sign

- Multiply equation (2) by -1

∴-7x-5y=-6 ⇒ (3)

- Add (1) and (3)

∴ -3x=6 ⇒ divide both sides by -3

∴ x=-2

- Substitute the value of x in (1) or (2)

∴ 4(-2)+5y=12

∴ -8+5y=12 ⇒ add 8 to both sides

∴ 5y=20 ⇒ divide each side by 5

∴ y = 4

- The solution of the system is the point which has the values of x and y

∴ The solution is (-2,4)