Math Problem Statement

y=

7x−20

y, equals, 2, x

y=

2x

Solution

You've given two equations for yy:

  1. y=7x20y = 7x - 20
  2. y=2xy = 2x

To find a solution, let's set the two expressions for yy equal to each other:

7x20=2x7x - 20 = 2x

Solving for xx:

  1. Subtract 2x2x from both sides: 7x2x=207x - 2x = 20 5x=205x = 20

  2. Divide both sides by 5: x=205=4x = \frac{20}{5} = 4

Now, find yy:

Substitute x=4x = 4 into either of the original equations (let's use y=2xy = 2x):

y=2(4)=8y = 2(4) = 8

Final solution:

x=4,y=8x = 4, \quad y = 8

Would you like more details or have any questions?

Here are 5 related questions:

  1. How do we solve for xx when the equation has more variables?
  2. Can we substitute y=8y = 8 in both equations to check consistency?
  3. How do we handle equations where the variable terms are on both sides?
  4. What happens if the equations are nonlinear?
  5. How can graphing these equations help visualize the solution?

Tip: Always simplify the equation as much as possible before solving for unknowns.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

y = mx + b (slope-intercept form)
Linear equation solution by substitution

Theorems

Equal values method
Solving systems of equations by substitution

Suitable Grade Level

Grades 6-8