9x+5y=-42
-2x+y=22
Find the ordered pairs
(multiplying the second equation by -5 to cancel the y's)
9x+5y=-42
10x-5y=-110
19x=-152
x=-8
Put that in either ORIGINAL equation to solve for y, and then your ordered pair would be (-8, y), replacing y with whatever you get for y.
To find the ordered pairs that satisfy this system of equations, we can use the method of substitution or elimination. Let's solve it using the elimination method.
First, let's multiply the second equation by 9, so that the coefficients of x in both equations are opposites:
-2x + y = 22
9(-2x + y) = 9 * 22
-18x + 9y = 198
Now we have the following system of equations:
9x + 5y = -42
-18x + 9y = 198
Next, we can add the two equations together to eliminate the x term:
(9x + 5y) + (-18x + 9y) = -42 + 198
-9x + 14y = 156
Simplifying further, we get:
-9x + 14y = 156
Now we have a new equation with just one variable. Let's solve it for y:
14y = 9x + 156
y = (9/14)x + (156/14)
y = (9/14)x + 78/7
Now that we have the value of y in terms of x, we can substitute this expression back into one of the original equations. Let's use the first equation:
9x + 5y = -42
9x + 5((9/14)x + 78/7) = -42
Simplifying further:
9x + (45/14)x + (390/7) = -42
126x + 45x + 780 = -588
Combining like terms:
171x + 780 = -588
Now, let's isolate x:
171x = -588 - 780
171x = -1368
x = -1368/171
x = -8
We have now found the value of x. We can substitute this value back into the equation we derived for y earlier:
y = (9/14)x + 78/7
y = (9/14)(-8) + 78/7
y = -72/14 + 78/7
y = -36/7 + 78/7
y = 42/7
y = 6
Therefore, the ordered pair that satisfies these equations is (-8, 6).