18. Systems of Equations and Matrices

Two Variable Systems of Linear Equations

18. Systems of Equations and Matrices

Two Variable Systems of Linear Equations

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Multiple Choice

Use the elimination method to solve the following system of linear equations.
$10x-4y=5$
$5x-4y=1$

$x=12,y=16$

$x=16,y=12$

$x=\frac34,y=\frac45$

$x=\frac45,y=\frac34$

Verified step by step guidance

Write down the given system of equations: 10x - 4y = 5 and 5x - 4y = 1.

Notice that the coefficients of y in both equations are the same. This makes it easier to eliminate y by subtracting the second equation from the first.

Subtract the second equation (5x - 4y = 1) from the first equation (10x - 4y = 5) to eliminate y. This results in a new equation: (10x - 5x) = (5 - 1).

Simplify the new equation to find the value of x. This will give you an equation in terms of x only.

Substitute the value of x back into one of the original equations to solve for y. Choose either equation and solve for y to find the complete solution for the system.