How do you solve the following system using substitution?: $3x - 2 y = 5, x+ 4 y = 4$

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How do you solve the following system using substitution?: $3x - 2 y = 5, x+ 4 y = 4$

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Answer 1 · 2018-03-18T04:17:09

The point of intersection is $(2,1/2)$ .

Explanation:

Solve system of equations:

$"Equation 1":$ $3x-2y=5$

$"Equation 2":$ $x+4y=4$

The two equations are linear equations in standard form. The solved values for $x$ and $y$ will be the point of intersection of the two lines.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve Equation 2 for $x$ .

Subtract $4y$ from both sides of the equation.

$x=4-4y$

Substitute $(4-4y)$ for $x$ in Equation 1 and solve for $y$ .

$3(4-4y)-2y=5$

Expand.

$12-12y-2y=5$

Simplify.

$12-14y=5$

Subtract $12$ from both sides of the equation.

$-14y=5-12$

Simplify.

$-14y=-7$

Divide both sides by $-14$ .

$y=(-7)/(-14)$

Simplify.

$y=1/2$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute $1/2$ for $y$ in Equation 2 and solve for $x$ .

$x+4(1/2)=4$

$x+cancel4^2(1/cancel2^1)=4$

Simplify.

$x+2=4$

Subtract $2$ from both sides.

$x=4-2$

Simplify.

$x=2$

The point of intersection is $(2,1/2)$ .

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How do you solve the following system using substitution?: $3x - 2 y = 5, x+ 4 y = 4$

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How do you solve the following system using substitution?: $3x - 2 y = 5, x+ 4 y = 4$