7. Systems of Equations & Matrices

Two Variable Systems of Linear Equations

7. Systems of Equations & 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

Start by writing down the given system of equations: $ 10x - 4y = 5 $ and $ 5x - 4y = 1 $.

Notice that both equations have the term $-4y$. To eliminate $y$, subtract the second equation from the first equation: $(10x - 4y) - (5x - 4y) = 5 - 1$.

Simplify the result of the subtraction: $10x - 5x = 5 - 1$, which simplifies to $5x = 4$.

Solve for $x$ by dividing both sides of the equation $5x = 4$ by 5: $x = \frac{4}{5}$.

Substitute $x = \frac{4}{5}$ back into either original equation to solve for $y$. For example, using $5x - 4y = 1$, substitute $x$ and solve for $y$.

4:27m

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Struggling with College Algebra?

Use the elimination method to solve the following system of linear equations.10x−4y=510x-4y=510x−4y=55x−4y=15x-4y=15x−4y=1

Watch next

Two Variable Systems of Linear Equations practice set

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