y = 2x and -3x + 8y = 26. Find the values of x and y.

Understand the Problem

The question involves solving a system of equations to find the values of x and y. We have one equation in slope-intercept form and another in standard form, and we need to determine the values of x and y that satisfy both equations.

Answer

The solution is \( (2, 4) \).

Steps to Solve

Substitute the value of y Since we have ( y = 2x ) from the first equation, we can substitute this into the second equation:

[ -3x + 8(2x) = 26 ]

Simplify the equation Now, simplify the equation:

[ -3x + 16x = 26 ]

Combine like terms Combine the ( x ) terms:

[ 13x = 26 ]

Solve for x Now, divide both sides by 13 to find ( x ):

[ x = \frac{26}{13} = 2 ]

Substitute x back to find y Now that we have ( x ), substitute ( x = 2 ) back into the first equation to find ( y ):

[ y = 2(2) = 4 ]

The solution is ( (2, 4) ).

More Information

This solution indicates that the values of ( x ) and ( y ) that satisfy both equations are ( 2 ) and ( 4 ), respectively. These values can be verified by plugging them back into the original equations.

Tips

Forgetting to substitute correctly when using both equations.
Miscalculating during the simplification of the equations.
Confusing the signs when combining like terms.

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