4x+5y=102 / 7x+5y=126

Question

i put the word problem into separate equations, all i have to do is solve the equations using the system of equations method.

Answer 1

notice that both equations have 5y; you can solve one equation for 5y and then plug that into the other equation.

So, the first equation would be:

5y=102-4x

 

Plug this into the second equation. and solve for x.

 

Please post here if you are stuck and have additional questions.

 

Answer 2

Hi - 

What you want to do here is solve the equation by substitution.

To do that, you solve one of the equations for y. then plug that into the other equation so you have an equation with only x as the variable.

 

1) Solve either equation for y.  Lets go with the first one:

4x+5y=102

Subtract 4x from each side:

5y=102-4x

Divide both sides by 5

y=(102-4x)/5

 

2) Plug this value for y into the other equation we started with:

7x+5y = 126

7x + 5((102-4x)/5) = 126

 

3) Solve the resulting equation for x.

Since we are multiplying and dividing (102-4x) by 5 the 2 5s cancel each other out

7x + 5((102-4x)/5) = 126

7x + 102 - 4x = 126

Combine the 2 x terms:

3x+102=126

subtract 102 from each side:

3x = 24

Divide both sides by 3:

x=8

 

Once we have a value for x, we can plug that number into either one of our starting equations to solve for y.

4x + 5y = 102; if x = 8

32+5y = 102

subtract 32 from each side:

5y = 70

Divide both sides by 5:

y = 14

 

So x = 8 and y = 14.

 

You can check your work by plugging these numbers both into your 2 initial equations.

4x+5y=102; 4*8+5*14 = 102

 

7x+5y=126; 7*8 +5*14 = 126

 

Thanks

Beth