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 substitution to solve the following system of linear equations.
$4x+2y=7$
$x+5y=4$

$\left(\frac12,\frac32\right)$

$\left(\frac32,\frac12\right)$

$\left(-\frac23,\frac13\right)$

$\left(-\frac13,\frac23\right)$

Verified step by step guidance

Start by identifying the two equations in the system: 4x + 2y = 7 and x + 5y = 4.

Choose one of the equations to solve for one variable in terms of the other. Let's solve the second equation, x + 5y = 4, for x. Subtract 5y from both sides to get x = 4 - 5y.

Substitute the expression for x from the second equation into the first equation. Replace x in 4x + 2y = 7 with 4 - 5y, resulting in 4(4 - 5y) + 2y = 7.

Simplify the equation from the previous step. Distribute the 4 to get 16 - 20y + 2y = 7. Combine like terms to simplify further: 16 - 18y = 7.

Solve for y by isolating it on one side of the equation. Subtract 16 from both sides to get -18y = 7 - 16, which simplifies to -18y = -9. Divide both sides by -18 to find the value of y.