Games
Problems
Go Pro!

# Three to Two

Pro Problems > Math > Algebra > Equations > Systems of Equations

## Three to Two

If 3x + 5y + z = 100, and 2z + 7x + 9y = 56, find the value of
y - x
.

Presentation mode
Problem by malimil

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Assign this problem

## Similar Problems

### b Over X + Y

The sum of two numbers is X2, and their difference is Y2. X is 4 more than Y. If the smaller of the two numbers is b, calculate
b
X + Y
.

### System of Equations with K

The following is a system of equations in x and y, with a constant K.

x + 2y = K

x - y = 2

If K is an integer between 20 and 25 inclusive, find all K such that the system has integer solutions.

### System in a System

3x + 4y = 16
2x - 2y = 6

Also,

xm + yn = 28
ym + xn = 22

Find the ordered pair (m, n).

### System of Three Equations

Find the ordered triple (x, y, z) if x + y + z = 16; x - z = 10; and y + z = 9

### Fractions within Fractions

Find all ordered pairs (x,y) such that:

1 +
2
x
+
1
x2
-
4
y2
1 +
1
x
+
2
y
= 1

1 +
2
x
+
1
x2
-
4
y2
1 +
1
x
-
2
y
= 2

### Three Numbers

The sum of three numbers is 78. If the first two numbers are doubled, the new sum is 128. Calculate the difference between the sum of the first two numbers and the third number

### Ugly Fractional System

Find the ordered pair (m,n) which solves the following system of equations.

2(-
19
2
m - n) = -30 - 14m + 3n

-13(-
1
4
n - 2) = -
9
2
m + 70 + 3n

### Find X + Y + Z

If 2X + 3Y + 4Z = 100 and 5X + 7Y + 9Z = 242, find X + Y + Z.

### P and Q

The sum of p and q is 44. q is two more than twice p.  Find the ordered pair (p, q).

### P and Q

p is 12 more than a third of q, which is 12 less than half of p.  Find the ordered pair (p, q)