Which system of linear equations has the ordered pair langle 4,-5rangle as a solution? 2x-5y=-30 and 7x+4y=-19 6x-y=-29 and 8x+3y=-17 3x-2y=22 and 2x+9y=-37 5x-6y=49 and x+8y=-27

To determine which system of linear equations has the ordered pair $\langle 4,-5\rangle$ as a solution, we need to substitute the values of $x$ and $y$ into each equation and check if the equations hold true.<br /><br />Let's start with the first system of equations:<br />$2x-5y=-30$ and $7x+4y=-19$<br /><br />Substituting $x=4$ and $y=-5$ into the first equation:<br />$2(4)-5(-5)=-30$<br />$8+25=-30$<br />$33\neq-30$<br /><br />Since the first equation does not hold true, we can conclude that the ordered pair $\langle 4,-5\rangle$ is not a solution to this system of equations.<br /><br />Now let's move on to the second system of equations:<br />$6x-y=-29$ and $8x+3y=-17$<br /><br />Substituting $x=4$ and $y=-5$ into the first equation:<br />$6(4)-(-5)=-29$<br />$24+5=-29$<br />$29\neq-29$<br /><br />Again, the first equation does not hold true, so the ordered pair $\langle 4,-5\rangle$ is not a solution to this system of equations either.<br /><br />Next, let's consider the third system of equations:<br />$3x-2y=22$ and $2x+9y=-37$<br /><br />Substituting $x=4$ and $y=-5$ into the first equation:<br />$3(4)-2(-5)=22$<br />$12+10=22$<br />$22=22$<br /><br />The first equation holds true, so let's substitute the values into the second equation:<br />$2(4)+9(-5)=-37$<br />$8-45=-37$<br />$-37=-37$<br /><br />Both equations hold true, so the ordered pair $\langle 4,-5\rangle$ is a solution to this system of equations.<br /><br />Finally, let's check the fourth system of equations:<br />$5x-6y=49$ and $x+8y=-27$<br /><br />Substituting $x=4$ and $y=-5$ into the first equation:<br />$5(4)-6(-5)=49$<br />$20+30=49$<br />$50\neq49$<br /><br />The first equation does not hold true, so the ordered pair $\langle 4,-5\rangle$ is not a solution to this system of equations.<br /><br />Therefore, the correct answer is the third system of equations:<br />$3x-2y=22$ and $2x+9y=-37$