Question

solve each system of equation using the graphing method

1. solve each system.

a. $y = -2x + 5$
$y = \frac{1}{8}x - \frac{7}{2}$
b. $3x - y = 5$
$4x - 2y = 4$
c. $y = -2x + 3$
$y = x$
d. $2x + y = 5$
$4x - 1 = y$

Explanation:

Step1: Set equations equal (a)

Set $-2x + 5 = \frac{1}{8}x - \frac{7}{2}$

Step2: Solve for x (a)

Multiply by 8: $-16x + 40 = x - 28$
$-17x = -68$
$x = 4$

Step3: Find y (a)

Substitute $x=4$ into $y=-2x+5$:
$y = -2(4) + 5 = -3$
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Step1: Rewrite in slope-intercept (b)

$y=3x-5$; $y=2x-2$

Step2: Set equal (b)

$3x - 5 = 2x - 2$

Step3: Solve for x (b)

$x = 3$

Step4: Find y (b)

Substitute $x=3$ into $y=3x-5$:
$y=3(3)-5=4$
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Step1: Set equations equal (c)

Set $-2x + 3 = x$

Step2: Solve for x (c)

$-3x = -3$
$x=1$

Step3: Find y (c)

Substitute $x=1$ into $y=x$:
$y=1$
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Step1: Rewrite in slope-intercept (d)

$y=-2x+5$; $y=4x-1$

Step2: Set equal (d)

$-2x + 5 = 4x - 1$

Step3: Solve for x (d)

$-6x = -6$
$x=1$

Step4: Find y (d)

Substitute $x=1$ into $y=-2x+5$:
$y=-2(1)+5=3$

Answer:

a. $(4, -3)$
b. $(3, 4)$
c. $(1, 1)$
d. $(1, 3)$