Question #95527

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Answer 1 · 2018-01-04T11:57:34

${(x = -3), (y = -4) :}$

Start by dividing both sides of the second equation by $-2$ . You will end up with

$(2y)/(-2) = 7/-2 + (5x)/-2$

$-y = -7/2 - (5x)/2$

Now, notice that the left-hand side of the two equations is equal.

${( -y = -5/7 - (11x)/7), (-y = -7/2 - (5x)/2) :}$

This means that you can equate the two right-hand sides to get an equation with one unknown, $x$ .

$-5/7 - (11x)/7 = -7/2 - (5x)/2$

DIvide or multiply both sides by $-1$ to get rid of the minus signs.

$5/7 + (11x)/7 = 7/2 + (5x)/2$

$(5 + 11x)/7 = (7 + 5x)/2$

Next, cross multiply, i.e. multiply the numerator of one fraction by the denominator of the second fraction and vice versa. You will end up with

$7 * (7 + 5x) = 2 * (5 + 11x)$

This will be equivalent o

$49 + 35x = 10 + 22x$

Subtract $22x$ and $49$ from both sides to get

$13x = - 39$

Finally, divide both sides by $13$ to isolate $x$

$x = -39/13 = -3$

Now that you have a value for $x$ , pick one of the two equations and use it to find the value of $y$ .

$2y = 7 + 5 * (-3)$

$2y = -8$

Divide both sides by $2$ to isolate $y$

$y = -4$

Therefore, your system of two equations with two unknowns has the solution set

${(x = -3), (y = -4) :}$

If you want, you can double-check the result by plugging in the two values into the original equations.

You will have

$-(-4) = -5/7 - (11 * (-3))/7$

$4 = (-5 + 33)/7" "color(green)(sqrt())$

and

$2 * (-4) = 7 + 5 * (-3)$

$-8 = 7 - 15" "color(green)(sqrt())$