How do I use a graph to solve the system of equations $3 x + 4 y = 10$ $3x+4y=10$ and $x - y = 1$ $x−y=1$ ?

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Answer 1 · 2015-07-09T19:42:41

You graph the equations and see where they intersect.

Your equations are

$3 x + 4 y = 10$ $3x+4y = 10$
$x - y = 1$ $x-y = 1$

Let's rearrange these to

(1) $y = \frac{1}{4} (10 - 3 x) = - \frac{3}{4} x + \frac{5}{2}$ $y = 1/4(10-3x) = -3/4 x + 5/2$
(2) $y = x - 1$ $y = x-1$

Plot the graph of Equation 1.

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Now add the graph for Equation 2.

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The two lines intersect at ( $2, 1$ $2,1$ ).

The solution is $x = 2$ $x = 2$ , $y = 1$ $y = 1$ .

Check:

$3 x + 4 y = 3 \times 2 + 4 \times 1 = 6 + 4 = 10$ $3x+4y = 3×2+4×1 = 6+4 = 10$

$x - y = 2 - 1 = 1$ $x-y = 2-1 = 1$

How do I use a graph to solve the system of equations 3x+4y=103x+4y=103x+4y=10 and x−y=1x−y=1x−y=1?